.. default-domain:: dynare

.. |br| raw:: html

    <br>

###########
Time Series
###########

Dynare provides a MATLAB/Octave class for handling time series data,
which is based on a class for handling dates. Dynare also provides a
new type for dates, so that the user does not have to worry about
class and methods for dates. Below, you will first find the class and
methods used for creating and dealing with dates and then the class
used for using time series. Dynare also provides an interface to the
X-13 ARIMA-SEATS seasonal adjustment program produced, distributed, and
maintained by the U.S. Census Bureau (2020).


Dates
=====
.. highlight:: matlab

.. _dates in a mod file:

Dates in a mod file
-------------------

Dynare understands dates in a mod file. Users can declare annual, bi-annual,
quarterly, or monthly dates using the following syntax::

    1990Y
    1990A
    1990S2
    1990H2
    1990Q4
    1990M11

Note that there are two syntaxes for annual dates (`1990A` is equivalent to
`1990Y`), and for bi-annual dates (`1990H2` is equivalent to `1990S2`).

Behind the scene, Dynare’s preprocessor translates these expressions
into instantiations of the MATLAB/Octave’s class ``dates`` described
below. Basic operations can be performed on dates:

**plus binary operator (+)**

    An integer scalar, interpreted as a number of periods, can be
    added to a date. For instance, if ``a = 1950Q1`` then ``b =
    1951Q2`` and ``b = a + 5`` are identical.

**plus unary operator (+)**

    Increments a date by one period. ``+1950Q1`` is identical to
    ``1950Q2``, ``++++1950Q1`` is identical to ``1951Q1``.

**minus binary operator (-)**

    Has two functions: difference and subtraction. If the second
    argument is a date, calculates the difference between the first
    date and the second date (e.g. ``1951Q2-1950Q1`` is equal to
    ``5``). If the second argument is an integer ``X``, subtracts
    ``X`` periods from the date (e.g. ``1951Q2-2`` is equal to
    ``1950Q4``).

**minus unary operator (-)**

    Subtracts one period to a date. ``-1950Q1`` is identical to
    ``1949Q4``. The unary minus operator is the reciprocal of the
    unary plus operator, ``+-1950Q1`` is identical to ``1950Q1``.

**colon operator (:)**

    Can be used to create a range of dates. For instance, ``r =
    1950Q1:1951Q1`` creates a ``dates`` object with five elements:
    ``1950Q1``, ``1950Q2``, ``1950Q3``, ``1950Q4`` and ``1951Q1``. By default the
    increment between each element is one period. This default can be
    changed using, for instance, the following instruction:
    ``1950Q1:2:1951Q1`` which will instantiate a ``dates`` object with
    three elements: ``1950Q1``, ``1950Q3`` and ``1951Q1``.

**horzcat operator ([,])**

    Concatenates dates objects without removing repetitions. For
    instance ``[1950Q1, 1950Q2]`` is a ``dates`` object with two
    elements (``1950Q1`` and ``1950Q2``).

**vertcat operator ([;])**

    Same as ``horzcat`` operator.

**eq operator (equal, ==)**

    Tests if two ``dates`` objects are equal. ``+1950Q1==1950Q2``
    returns ``true``, ``1950Q1==1950Q2`` returns ``false``. If the compared
    objects have both ``n>1`` elements, the ``eq`` operator returns a
    column vector, ``n`` by ``1``, of logicals.

**ne operator (not equal, ~=)**

    Tests if two ``dates`` objects are not equal. ``+1950Q1~=``
    returns ``false`` while ``1950Q1~=1950Q2`` returns ``true``. If the
    compared objects both have ``n>1`` elements, the ``ne`` operator
    returns an ``n`` by ``1`` column vector of logicals.

**lt operator (less than, <)**

    Tests if a ``dates`` object preceeds another ``dates`` object. For
    instance, ``1950Q1<1950Q3`` returns ``true``. If the compared objects
    have both ``n>1`` elements, the ``lt`` operator returns a column
    vector, ``n`` by ``1``, of logicals.

**gt operator (greater than, >)**

    Tests if a ``dates`` object follows another ``dates`` object. For
    instance, ``1950Q1>1950Q3`` returns ``false``. If the compared objects
    have both ``n>1`` elements, the ``gt`` operator returns a column
    vector, ``n`` by ``1``, of logicals.

**le operator (less or equal, <=)**

    Tests if a ``dates`` object preceeds another ``dates`` object or
    is equal to this object. For instance, ``1950Q1<=1950Q3`` returns
    ``true``. If the compared objects have both ``n>1`` elements, the
    ``le`` operator returns a column vector, ``n`` by ``1``, of logicals.

**ge operator (greater or equal, >=)**

    Tests if a ``dates`` object follows another ``dates`` object or is
    equal to this object. For instance, ``1950Q1>=1950Q3`` returns
    ``false``. If the compared objects have both ``n>1`` elements, the
    ``ge`` operator returns a column vector, ``n`` by ``1``, of logicals.

One can select an element, or some elements, in a ``dates`` object as
he would extract some elements from a vector in MATLAB/Octave. Let ``a
= 1950Q1:1951Q1`` be a ``dates`` object, then ``a(1)==1950Q1`` returns
``true``, ``a(end)==1951Q1`` returns ``true`` and ``a(end-1:end)`` selects
the two last elements of ``a`` (by instantiating the ``dates`` object
``[1950Q4, 1951Q1]``).

Remark: Dynare substitutes any occurrence of dates in the ``.mod`` file
into an instantiation of the ``dates`` class regardless of the
context. For instance, ``d = 1950Q1`` will be translated as ``d =
dates('1950Q1');``. This automatic substitution can lead to a crash if
a date is defined in a string. Typically, if the user wants to display
a date::

    disp('Initial period is 1950Q1');

Dynare will translate this as::

    disp('Initial period is dates('1950Q1')');

which will lead to a crash because this expression is illegal in
MATLAB/Octave. For this situation, Dynare provides the ``$`` escape
parameter. The following expression::

    disp('Initial period is $1950Q1');

will be translated as::

    disp('Initial period is 1950Q1');

in the generated MATLAB/Octave script.


.. _dates-members:

The dates class
---------------

.. class:: dates

    :arg freq: equal to 1, 2, 4, 12 or 365 (resp. for annual, bi-annual, quarterly,
               monthly, or daily dates).
    :arg time: a ``n*1`` array of integers, the number of periods since year 0 ().

    Each member is private, one can display the content of a member
    but cannot change its value directly. Note also that it is not
    possible to mix frequencies in a ``dates`` object: all the
    elements must have common frequency.

    The ``dates`` class has the following constructors:

    .. construct:: dates()
                   dates(FREQ)

        |br| Returns an empty ``dates`` object with a given frequency
        (if the constructor is called with one input
        argument). ``FREQ`` is a character equal to ’Y’ or ’A’ for
        annual dates, ’S’ or ’H’ for bi-annual dates, ’Q’ for
        quarterly dates, ’M’ for monthly dates, or ’D’ for daily
        dates. Note that ``FREQ`` is not case sensitive, so that, for
        instance, ’q’ is also allowed for quarterly dates. The
        frequency can also be set with an integer scalar equal to 1
        (annual), 2 (bi-annual), 4 (quarterly), 12 (monthly), or 365
        (daily). The instantiation of empty objects can be used to
        rename the ``dates`` class. For instance, if one only works
        with quarterly dates, object ``qq`` can be created as::

            qq = dates('Q')

        and a ``dates`` object holding the date ``2009Q2``::

            d0 = qq(2009,2);

        which is much simpler if ``dates`` objects have to be defined
        programmatically. For daily dates, we would instantiate an
        empty daily dates object as::

            dd = dates('D')

        and a ``dates`` object holding the date ``2020-12-31``::

            d1 = dd(2020,12,31);


    .. construct:: dates(STRING)
                   dates(STRING, STRING, ...)

        |br| Returns a ``dates`` object that represents a date as
        given by the string ``STRING``. This string has to be
        interpretable as a date (only strings of the following forms
        are admitted: ``'1990Y'``, ``'1990A'``, ``1990S1``,
        ``1990H1``, ``'1990Q1'``, ``'1990M2'``, or ``'2020-12-31'``),
        the routine ``isdate`` can be used to test if a string is
        interpretable as a date. If more than one argument is
        provided, they should all be dates represented as strings, the
        resulting ``dates`` object contains as many elements as
        arguments to the constructor. For the daily dates, the string
        must be of the form yyyy-mm-dd with two digits for the
        months (mm) and days (dd), even if the number of days or
        months is smaller than ten (in this case a leading 0 is
        required).


    .. construct:: dates(DATES)
                   dates(DATES, DATES, ...)

        |br| Returns a copy of the ``dates`` object ``DATES`` passed
        as input arguments. If more than one argument is provided,
        they should all be ``dates`` objects. The number of elements
        in the instantiated ``dates`` object is equal to the sum of
        the elements in the ``dates`` passed as arguments to the
        constructor.


    .. construct:: dates (FREQ, YEAR, SUBPERIOD[, S])

        |br| where ``FREQ`` is a single character (’Y’, ’A’, ’S’, ’H’,
        ’Q’, ’M’, ’D’) or integer (1, 2, 4, 12, or 365) specifying the
        frequency, ``YEAR`` and ``SUBPERIOD`` and ``S`` are ``n*1``
        vectors of integers. Returns a ``dates`` object with ``n``
        elements. The last argument, ``S``, is only to be used for
        daily frequency. If ``FREQ`` is equal to ``'Y'``, ``'A'`` or
        ``1``, the third argument is not needed (because ``SUBPERIOD``
        is necessarily a vector of ones in this case).


    *Example*

        ::

            do1 = dates('1950Q1');
            do2 = dates('1950Q2','1950Q3');
            do3 = dates(do1,do2);
            do4 = dates('Q',1950, 1);
            do5 = dates('D',1973, 1, 25);

    |br|

    A ``dates`` object with multiple elements can be considered a one-dimensional array of dates. Standard array operations can be applied to a ``dates`` object:

     - square brackets can be used to concatenate dates objects::

         >> A = dates('1938Q4');
         >> B = dates('1945Q3');
         >> C = [A, B];

     - semicolons can be used to create ranges of dates::

         >> A = dates('2009Q2');
         >> B = A:A+2;
         >> B

         B = <dates: 2009Q2, 2009Q3, 2009Q4>

     - objects can be indexed by an integer or a vector of integer::

         >> B(1)

         ans = <dates: 2009Q2>

         >> B(end)

         ans = <dates: 2009Q4>

         >> B(1:2)

         ans = <dates: 2009Q2, 2009Q3>

    |br|

    A list of the available methods, by alphabetical order, is given
    below. Note that by default the methods do not allow in place
    modifications: when a method is applied to an object a new object
    is instantiated. For instance, to apply the method
    ``multiplybytwo`` to an object ``X`` we write::

      >> X = 2;
      >> Y = X.multiplybytwo();
      >> X

      2

      >> Y

      4


    or equivalently::

        >> Y = multiplybytwo(X);

    the object ``X`` is left unchanged, and the object ``Y`` is a
    modified copy of ``X`` (multiplied by two). This behaviour is
    altered if the name of the method is postfixed with an
    underscore. In this case the creation of a copy is avoided. For
    instance, following the previous example, we would have::

      >> X = 2;
      >> X.multiplybytwo_();
      >> X

      4

    Modifying the objects in place, with underscore methods, is
    particularly useful if the methods are called in loops, since this
    saves the object instantiation overhead.

    |br|

    .. datesmethod:: C = append (A, B)
                     append_ (A, B)

        |br| Appends ``dates`` object ``B``, or a string that can be
        interpreted as a date, to the ``dates`` object ``A``. If ``B``
        is a ``dates`` object it is assumed that it has no more than
        one element.

        *Example*

            ::

                >> D = dates('1950Q1','1950Q2');
                >> d = dates('1950Q3');
                >> E = D.append(d);
                >> F = D.append('1950Q3');
                >> isequal(E,F)

                ans =

                     1
                >> F

                F = <dates: 1950Q1, 1950Q2, 1950Q3>

                >> D

                D = <dates: 1950Q1, 1950Q2>

                >> D.append_('1950Q3')

                ans = <dates: 1950Q1, 1950Q2, 1950Q3>


    .. datesmethod:: B = char (A)

        |br| Overloads the MATLAB/Octave ``char`` function. Converts a
        ``dates`` object into a character array.

        *Example*

            ::

                >> A = dates('1950Q1');
                > A.char()

                ans =

                '1950Q1'


    .. datesmethod:: C = colon (A, B)
                     C = colon (A, i, B)

        |br| Overloads the MATLAB/Octave colon (``:``) operator. A and
        B are ``dates`` objects. The optional increment ``i`` is a
        scalar integer (default value is ``i=1``). This method returns
        a ``dates`` object and can be used to create ranges of dates.

        *Example*

            ::

                >> A = dates('1950Q1');
                >> B = dates('1951Q2');
                >> C = A:B

                C = <dates: 1950Q1, 1950Q2, 1950Q3, 1950Q4, 1951Q1>

                >> D = A:2:B

                D = <dates: 1950Q1, 1950Q3, 1951Q1>


    .. datesmethod:: B = copy (A)

        |br| Returns a copy of a ``dates`` object.


    .. datesmethod:: disp (A)

        |br| Overloads the MATLAB/Octave disp function for ``dates`` object.


    .. datesmethod:: display (A)

        |br| Overloads the MATLAB/Octave display function for ``dates`` object.

        *Example*

            ::

                >> disp(B)

                B = <dates: 1950Q1, 1950Q2, 1950Q3, 1950Q4, 1951Q1, 1951Q2, 1951Q3, 1951Q4, 1952Q1, 1952Q2, 1952Q3>


                >> display(B)

                B = <dates: 1950Q1, 1950Q2, ..., 1952Q2, 1952Q3>


    .. datesmethod:: B = double (A)

        |br| Overloads the MATLAB/Octave ``double`` function. ``A`` is
        a ``dates`` object. The method returns a floating point
        representation of a ``dates`` object, the integer and
        fractional parts respectively corresponding to the year and
        the subperiod. The fractional part is the subperiod number
        minus one divided by the frequency (``1``, ``4``, or ``12``).

        *Example*:

            ::

                >> a = dates('1950Q1'):dates('1950Q4');
                >> a.double()

                ans =

                     1950.00
                     1950.25
                     1950.50
                     1950.75


    .. datesmethod:: C = eq (A, B)

        |br| Overloads the MATLAB/Octave ``eq`` (equal, ``==``)
        operator. ``dates`` objects ``A`` and ``B`` must have the same
        number of elements (say, ``n``). The returned argument is a
        ``n`` by ``1`` vector of logicals. The i-th element of
        ``C`` is equal to ``true`` if and only if the dates ``A(i)`` and
        ``B(i)`` are the same.

        *Example*

            ::

                >> A = dates('1950Q1','1951Q2');
                >> B = dates('1950Q1','1950Q2');
                >> A==B

                ans =

                  2x1 logical array

                   1
                   0


    .. datesmethod:: C = ge (A, B)

        |br| Overloads the MATLAB/Octave ``ge`` (greater or equal,
        ``>=``) operator. ``dates`` objects ``A`` and ``B`` must have
        the same number of elements (say, ``n``). The returned
        argument is a ``n`` by ``1`` vector of logicals. The
        i-th element of ``C`` is equal to ``true`` if and only if the
        date ``A(i)`` is posterior or equal to the date ``B(i)``.

        *Example*

            ::

                >> A = dates('1950Q1','1951Q2');
                >> B = dates('1950Q1','1950Q2');
                >> A>=B

                ans =

                  2x1 logical array

                   1
                   1


    .. datesmethod:: C = gt (A, B)

        |br| Overloads the MATLAB/Octave ``gt`` (greater than, ``>``)
        operator. ``dates`` objects ``A`` and ``B`` must have the same
        number of elements (say, ``n``). The returned argument is a
        ``n`` by ``1`` vector of logicals. The i-th element of
        ``C`` is equal to ``1`` if and only if the date ``A(i)`` is
        posterior to the date ``B(i)``.

        *Example*

            ::

                >> A = dates('1950Q1','1951Q2');
                >> B = dates('1950Q1','1950Q2');
                >> A>B

                ans =

                  2x1 logical array

                   0
                   1


    .. datesmethod:: D = horzcat (A, B, C, ...)

        |br| Overloads the MATLAB/Octave ``horzcat`` operator. All the
        input arguments must be ``dates`` objects. The returned
        argument is a ``dates`` object gathering all the dates given
        in the input arguments (repetitions are not removed).

        *Example*

            ::

                >> A = dates('1950Q1');
                >> B = dates('1950Q2');
                >> C = [A, B];
                >> C

                C = <dates: 1950Q1, 1950Q2>


    .. datesmethod:: C = intersect (A, B)

        |br| Overloads the MATLAB/Octave ``intersect`` function. All
        the input arguments must be ``dates`` objects. The returned
        argument is a ``dates`` object gathering all the common dates
        given in the input arguments. If ``A`` and ``B`` are disjoint
        ``dates`` objects, the function returns an empty ``dates``
        object. Returned dates in ``dates`` object ``C`` are sorted by
        increasing order.

        *Example*

            ::

                >> A = dates('1950Q1'):dates('1951Q4');
                >> B = dates('1951Q1'):dates('1951Q4');
                >> C = intersect(A, B);
                >> C

                C = <dates: 1951Q1, 1951Q2, 1951Q3, 1951Q4>


    .. datesmethod:: B = isempty (A)

        |br| Overloads the MATLAB/Octave ``isempty`` function.

        *Example*

            ::

                >> A = dates('1950Q1');
                >> A.isempty()

                ans =

                  logical

                  0

                >> B = dates();
                >> B.isempty()

                ans =

                  logical

                  1

    .. datesmethod:: C = isequal (A, B)

        |br| Overloads the MATLAB/Octave ``isequal`` function.

        *Example*

            ::

                >> A = dates('1950Q1');
                >> B = dates('1950Q2');
                >> isequal(A, B)

                ans =

                  logical

                  0


    .. datesmethod:: C = le (A, B)

        |br| Overloads the MATLAB/Octave ``le`` (less or equal,
        ``<=``) operator. ``dates`` objects ``A`` and ``B`` must have
        the same number of elements (say, ``n``). The returned
        argument is a ``n`` by ``1`` vector of logicals. The
        i-th element of ``C`` is equal to ``true`` if and only if the
        date ``A(i)`` is anterior or equal to the date ``B(i)``.

        *Example*

            ::

                >> A = dates('1950Q1','1951Q2');
                >> B = dates('1950Q1','1950Q2');
                >> A<=B

                ans =

                  2x1 logical array

                   1
                   0


    .. datesmethod:: B = length (A)

        |br| Overloads the MATLAB/Octave ``length`` function. Returns
        the number of elements in a ``dates`` object.

        *Example*

            ::

                >> A = dates('1950Q1'):dates(2000Q3);
                >> A.length()

                ans =

                   203


    .. datesmethod:: C = lt (A, B)

        |br| Overloads the MATLAB/Octave ``lt`` (less than,
        ``<``) operator. ``dates`` objects ``A`` and ``B`` must have
        the same number of elements (say, ``n``). The returned
        argument is a ``n`` by ``1`` vector of logicals. The
        i-th element of ``C`` is equal to ``true`` if and only if the
        date ``A(i)`` is anterior or equal to the date ``B(i)``.

        *Example*

            ::

                >> A = dates('1950Q1','1951Q2');
                >> B = dates('1950Q1','1950Q2');
                >> A<B

                ans =

                  2x1 logical array

                   0
                   0


    .. datesmethod:: D = max (A, B, C, ...)

        |br| Overloads the MATLAB/Octave ``max`` function. All input
        arguments must be ``dates`` objects. The function returns a
        single element ``dates`` object containing the greatest date.

        *Example*

            ::

                >> A = {dates('1950Q2'), dates('1953Q4','1876Q2'), dates('1794Q3')};
                >> max(A{:})

                ans = <dates: 1953Q4>


    .. datesmethod:: D = min (A, B, C, ...)

        |br| Overloads the MATLAB/Octave ``min`` function. All input
        arguments must be ``dates`` objects. The function returns a
        single element ``dates`` object containing the smallest date.

        *Example*

            ::

                >> A = {dates('1950Q2'), dates('1953Q4','1876Q2'), dates('1794Q3')};
                >> min(A{:})

                ans = <dates: 1794Q3>


    .. datesmethod:: C = minus (A, B)

        |br| Overloads the MATLAB/Octave ``minus`` operator
        (``-``). If both input arguments are ``dates`` objects, then
        number of periods between ``A`` and ``B`` is returned (so that
        ``A+C=B``). If ``B`` is a vector of integers, the minus
        operator shifts the ``dates`` object by ``B`` periods
        backward.

        *Example*

            ::

                >> d1 = dates('1950Q1','1950Q2','1960Q1');
                >> d2 = dates('1950Q3','1950Q4','1960Q1');
                >> ee = d2-d1

                ee =

                     2
                     2
                     0

                >> d1-(-ee)

                ans = <dates: 1950Q3, 1950Q4, 1960Q1>


    .. datesmethod:: C = mtimes (A, B)

        |br| Overloads the MATLAB/Octave ``mtimes`` operator
        (``*``). ``A`` and ``B`` are respectively expected to be a
        ``dates`` object and a scalar integer. Returns ``dates``
        object ``A`` replicated ``B`` times.

        *Example*

            ::

                >> d = dates('1950Q1');
                >> d*2

                ans = <dates: 1950Q1, 1950Q1>


    .. datesmethod:: C = ne (A, B)

        |br| Overloads the MATLAB/Octave ``ne`` (not equal, ``~=``)
        operator. ``dates`` objects ``A`` and ``B`` must have the same
        number of elements (say, ``n``) or one of the inputs must be a
        single element ``dates`` object. The returned argument is a
        ``n`` by ``1`` vector of logicals. The i-th element of
        ``C`` is equal to ``true`` if and only if the dates ``A(i)`` and
        ``B(i)`` are different.

        *Example*

            ::

                >> A = dates('1950Q1','1951Q2');
                >> B = dates('1950Q1','1950Q2');
                >> A~=B

                ans =

                  2x1 logical array

                   0
                   1


    .. datesmethod:: C = plus (A, B)

        |br| Overloads the MATLAB/Octave ``plus`` operator (``+``). If
        both input arguments are ``dates`` objects, then the method
        combines ``A`` and ``B`` without removing repetitions. If
        ``B`` is a vector of integers, the ``plus`` operator shifts
        the ``dates`` object by ``B`` periods forward.

        *Example*

            ::

                >> d1 = dates('1950Q1','1950Q2')+dates('1960Q1');
                >> d2 = (dates('1950Q1','1950Q2')+2)+dates('1960Q1');
                >> ee = d2-d1;

                ee =

                     2
                     2
                     0

                >> d1+ee
                ans = <dates: 1950Q3, 1950Q4, 1960Q1>


    .. datesmethod:: C = pop (A)
                     C = pop (A, B)
                     pop_ (A)
                     pop_ (A, B)

        |br| Pop method for ``dates`` class. If only one input is
        provided, the method removes the last element of a ``dates``
        object. If a second input argument is provided, a scalar
        integer between ``1`` and ``A.length()``, the method removes
        element number ``B`` from ``dates`` object ``A``.

        *Example*

            ::

                >> d = dates('1950Q1','1950Q2');
                >> d.pop()

                ans = <dates: 1950Q1>

                >> d.pop_(1)

                ans = <dates: 1950Q2>


    .. datesmethod:: C = remove (A, B)
                     remove_ (A, B)

        |br| Remove method for ``dates`` class. Both inputs have to be ``dates`` objects, removes dates in ``B`` from ``A``.

        *Example*

            ::

                >> d = dates('1950Q1','1950Q2');
                >> d.remove(dates('1950Q2'))

                ans = <dates: 1950Q1>


    .. datesmethod:: C = setdiff (A, B)

        |br| Overloads the MATLAB/Octave ``setdiff`` function. All the
        input arguments must be ``dates`` objects. The returned
        argument is a ``dates`` object all dates present in ``A`` but
        not in ``B``. If ``A`` and ``B`` are disjoint ``dates``
        objects, the function returns ``A``. Returned dates in
        ``dates`` object ``C`` are sorted by increasing order.

        *Example*

            ::

                >> A = dates('1950Q1'):dates('1969Q4');
                >> B = dates('1960Q1'):dates('1969Q4');
                >> C = dates('1970Q1'):dates('1979Q4');
                >> setdiff(A, B)

                ans = <dates: 1950Q1, 1950Q2,  ..., 1959Q3, 1959Q4>

                >> setdiff(A, C)

                ans = <dates: 1950Q1, 1950Q2,  ..., 1969Q3, 1969Q4>


    .. datesmethod:: B = sort (A)
                     sort_ (A)

        |br| Sort method for ``dates`` objects. Returns a ``dates`` object
        with elements sorted by increasing order.

        *Example*

            ::

                >> dd = dates('1945Q3','1938Q4','1789Q3');
                >> dd.sort()

                ans = <dates: 1789Q3, 1938Q4, 1945Q3>


    .. datesmethod:: B = strings (A)

        |br| Converts a ``dates`` object into a cell of char arrays.

        *Example*

            ::

                >> A = dates('1950Q1');
                >> A = A:A+1;
                >> A.strings()

                  ans =

                    1x2 cell array

                    {'1950Q1'}    {'1950Q2'}


    .. datesmethod:: B = subperiod (A)

        |br| Returns the subperiod of a date (an integer scalar
        between 1 and ``A.freq``). This method is not implemented for
        daily dates.

        *Example*

            ::

                >> A = dates('1950Q2');
                >> A.subperiod()

                ans =

                     2


    .. datesmethod:: B = uminus (A)

        |br| Overloads the MATLAB/Octave unary minus operator. Returns
        a ``dates`` object with elements shifted one period backward.

        *Example*

        ::

                >> dd = dates('1945Q3','1938Q4','1973Q1');
                >> -dd

                ans = <dates: 1945Q2, 1938Q3, 1972Q4>


    .. datesmethod:: D = union (A, B, C, ...)

        |br| Overloads the MATLAB/Octave ``union`` function. Returns a
        ``dates`` object with elements sorted by increasing order
        (repetitions are removed, to keep the repetitions use the
        ``horzcat`` or ``plus`` operators).

        *Example*

            ::

                >> d1 = dates('1945Q3','1973Q1','1938Q4');
                >> d2 = dates('1973Q1','1976Q1');
                >> union(d1,d2)

                ans = <dates: 1938Q4, 1945Q3, 1973Q1, 1976Q1>


    .. datesmethod:: B = unique (A)
                     unique_ (A)

        |br| Overloads the MATLAB/Octave ``unique`` function. Returns
        a ``dates`` object with repetitions removed (only the last
        occurence of a date is kept).

        *Example*

            ::

                >> d1 = dates('1945Q3','1973Q1','1945Q3');
                >> d1.unique()

                ans = <dates: 1973Q1, 1945Q3>


    .. datesmethod:: B = uplus (A)

        |br| Overloads the MATLAB/Octave unary plus operator. Returns
        a ``dates`` object with elements shifted one period ahead.

        *Example*

            ::

                >> dd = dates('1945Q3','1938Q4','1973Q1');
                >> +dd

                ans = <dates: 1945Q4, 1939Q1, 1973Q2>


    .. datesmethod:: D = vertcat (A, B, C, ...)

        |br| Overloads the MATLAB/Octave ``horzcat`` operator. All the
        input arguments must be ``dates`` objects. The returned
        argument is a ``dates`` object gathering all the dates given
        in the input arguments (repetitions are not removed).


    .. datesmethod:: B = year (A)

        |br| Returns the year of a date (an integer scalar
        between 1 and ``A.freq``).

        *Example*

            ::

                >> A = dates('1950Q2');
                >> A.subperiod()

                ans =

                       1950

.. _dseries-members:

The dseries class
=================

.. class:: dseries

    |br| The MATLAB/Octave ``dseries`` class handles time series
    data. As any MATLAB/Octave statements, this class can be used in a
    Dynare’s mod file. A ``dseries`` object has six members:

    :arg name: A ``vobs*1`` cell of strings or a ``vobs*p`` character array, the names of the variables.
    :arg tex: A ``vobs*1`` cell of strings or a ``vobs*p`` character array, the tex names of the variables.
    :arg dates dates: An object with ``nobs`` elements, the dates of the sample.
    :arg double data: A ``nobs`` by ``vobs`` array, the data.
    :arg ops: The history of operations on the variables.
    :arg tags: The user-defined tags on the variables.

    ``data``, ``name``, ``tex``, and ``ops`` are private members. The following
    constructors are available:

    .. construct:: dseries ()
                   dseries (INITIAL_DATE)

        |br| Instantiates an empty ``dseries`` object with, if
        defined, an initial date given by the single element ``dates``
        object *INITIAL_DATE.*

    .. construct:: dseries (FILENAME[, INITIAL_DATE])

        |br| Instantiates and populates a ``dseries`` object with a
        data file specified by *FILENAME*, a string passed as
        input. Valid file types are ``.m``, ``.mat``, ``.csv`` and
        ``.xls/.xlsx`` (Octave only supports ``.xlsx`` files and the
        `io <https://octave.sourceforge.io/io/>`__ package from
        Octave-Forge must be installed). The extension of the file
        should be explicitly provided.

        A typical ``.m`` file will have the following form::

            FREQ__ = 4;
            INIT__ = '1994Q3';
            NAMES__ = {'azert';'yuiop'};
            TEX__ = {'azert';'yuiop'};

            azert = randn(100,1);
            yuiop = randn(100,1);

        If a ``.mat`` file is used instead, it should provide the same
        informations, except that the data should not be given as a
        set of vectors, but as a single matrix of doubles named
        ``DATA__``. This array should have as many columns as elements
        in ``NAMES__`` (the number of variables). Note that the
        ``INIT__`` variable can be either a ``dates`` object or a
        string which could be used to instantiate the same ``dates``
        object. If ``INIT__`` is not provided in the ``.mat`` or
        ``.m`` file, the initial is by default set equal to
        ``dates('1Y')``. If a second input argument is passed to the
        constructor, ``dates`` object *INITIAL_DATE*, the initial date
        defined in *FILENAME* is reset to *INITIAL_DATE*. This is
        typically usefull if ``INIT__`` is not provided in the data
        file.

        If an ``.xlsx`` file is used, the first row should be a header
        containing the variable names. The first column may contain date
        information that must correspond to a valid date format recognized
        by Dynare. If such date information is specified in the first column,
        its header name must be left empty.

    .. construct:: dseries (DATA_MATRIX[,INITIAL_DATE[,LIST_OF_NAMES[,TEX_NAMES]]])
                   dseries (DATA_MATRIX[,RANGE_OF_DATES[,LIST_OF_NAMES[,TEX_NAMES]]])

        |br| If the data is not read from a file, it can be provided
        via a :math:`T \times N` matrix as the first argument to
        ``dseries`` ’ constructor, with :math:`T` representing the
        number of observations on :math:`N` variables. The optional
        second argument, *INITIAL_DATE*, can be either a ``dates``
        object representing the period of the first observation or a
        string which would be used to instantiate a ``dates``
        object. Its default value is ``dates('1Y')``. The optional
        third argument, *LIST_OF_NAMES*, is a :math:`N \times 1` cell
        of strings with one entry for each variable name. The default
        name associated with column ``i`` of *DATA_MATRIX* is
        ``Variable_i``. The final argument, *TEX_NAMES*, is a :math:`N
        \times 1` cell of strings composed of the LaTeX names
        associated with the variables. The default LaTeX name
        associated with column ``i`` of *DATA_MATRIX* is
        ``Variable\_i``. If the optional second input argument is a
        range of dates, ``dates`` object *RANGE_OF_DATES*, the number
        of rows in the first argument must match the number of
        elements *RANGE_OF_DATES* or be equal to one (in which case
        the single observation is replicated).

    .. construct:: dseries (TABLE)

       Creates a ``dseries`` object given the MATLAB Table provided as the sole
       argument. It is assumed that the first column of the table contains the
       dates of the ``dseries`` and the first row contains the names. This
       feature is not available under Octave.

       *Example*

       Various ways to create a ``dseries`` object::

         do1 = dseries(1999Q3);
         do2 = dseries('filename.csv');
         do3 = dseries([1; 2; 3], 1999Q3, {'var123'}, {'var_{123}'});

         >> do1 = dseries(dates('1999Q3'));
         >> do2 = dseries('filename.csv');
         >> do3 = dseries([1; 2; 3], dates('1999Q3'), {'var123'}, {'var_{123}'});


    One can easily create subsamples from a ``dseries`` object using
    the overloaded parenthesis operator. If ``ds`` is a ``dseries``
    object with :math:`T` observations and ``d`` is a ``dates`` object
    with :math:`S<T` elements, such that :math:`\min(d)` is not
    smaller than the date associated to the first observation in
    ``ds`` and :math:`\max(d)` is not greater than the date associated
    to the last observation, then ``ds(d)`` instantiates a new
    ``dseries`` object containing the subsample defined by ``d``.

    A list of the available methods, by alphabetical order, is given
    below. As in the previous section the in place modifications
    versions of the methods are postfixed with an underscore.


    .. dseriesmethod:: A = abs (B)
                       abs_ (B)

        |br| Overloads the ``abs()`` function for ``dseries``
        objects. Returns the absolute value of the variables in
        dseries ``object`` ``B``.

        *Example*

            ::

                >> ts0 = dseries(randn(3,2),'1973Q1',{'A1'; 'A2'},{'A_1'; 'A_2'});
                >> ts1 = ts0.abs();
                >> ts0

                ts0 is a dseries object:

                       | A1       | A2
                1973Q1 | -0.67284 | 1.4367
                1973Q2 | -0.51222 | -0.4948
                1973Q3 | 0.99791  | 0.22677

                >> ts1

                ts1 is a dseries object:

                       | abs(A1) | abs(A2)
                1973Q1 | 0.67284 | 1.4367
                1973Q2 | 0.51222 | 0.4948
                1973Q3 | 0.99791 | 0.22677

        *Example (in-place modification version)*

            ::

                >> ts0 = dseries(randn(3,2),'1973Q1',{'A1'; 'A2'},{'A_1'; 'A_2'});
                >> ts0

                ts0 is a dseries object:

                       | A1       | A2
                1973Q1 | -0.67284 | 1.4367
                1973Q2 | -0.51222 | -0.4948
                1973Q3 | 0.99791  | 0.22677

                >> ts0.abs_();
                >> ts0

                ts0 is a dseries object:

                       | abs(A1) | abs(A2)
                1973Q1 | 0.67284 | 1.4367
                1973Q2 | 0.51222 | 0.4948
                1973Q3 | 0.99791 | 0.22677

    .. dseriesmethod:: [A, B] = align (A, B)
                       align_ (A, B)

        If ``dseries`` objects ``A`` and ``B`` are defined on
        different time ranges, this function extends ``A`` and/or
        ``B`` with NaNs so that they are defined on the same time
        range. Note that both ``dseries`` objects must have the same
        frequency.

        *Example*

            ::

                >> ts0 = dseries(rand(5,1),dates('2000Q1')); % 2000Q1 -> 2001Q1
                >> ts1 = dseries(rand(3,1),dates('2000Q4')); % 2000Q4 -> 2001Q2
                >> [ts0, ts1] = align(ts0, ts1);             % 2000Q1 -> 2001Q2
                >> ts0

                ts0 is a dseries object:

                       | Variable_1
                2000Q1 | 0.81472
                2000Q2 | 0.90579
                2000Q3 | 0.12699
                2000Q4 | 0.91338
                2001Q1 | 0.63236
                2001Q2 | NaN

                >> ts1

                ts1 is a dseries object:

                       | Variable_1
                2000Q1 | NaN
                2000Q2 | NaN
                2000Q3 | NaN
                2000Q4 | 0.66653
                2001Q1 | 0.17813
                2001Q2 | 0.12801

                >> ts0 = dseries(rand(5,1),dates('2000Q1')); % 2000Q1 -> 2001Q1
                >> ts1 = dseries(rand(3,1),dates('2000Q4')); % 2000Q4 -> 2001Q2
                >> align_(ts0, ts1);                         % 2000Q1 -> 2001Q2
                >> ts1

                ts1 is a dseries object:

                       | Variable_1
                2000Q1 | NaN
                2000Q2 | NaN
                2000Q3 | NaN
                2000Q4 | 0.66653
                2001Q1 | 0.17813
                2001Q2 | 0.12801


        *Example (in-place modification version)*

            ::

                >> ts0 = dseries(rand(5,1),dates('2000Q1')); % 2000Q1 -> 2001Q1
                >> ts1 = dseries(rand(3,1),dates('2000Q4')); % 2000Q4 -> 2001Q2
                >> ts0

                ts0 is a dseries object:

                       | Variable_1
                2000Q1 | 0.80028
                2000Q2 | 0.14189
                2000Q3 | 0.42176
                2000Q4 | 0.91574
                2001Q1 | 0.79221

                >> ts1

                ts1 is a dseries object:

                       | Variable_1
                2000Q4 | 0.95949
                2001Q1 | 0.65574
                2001Q2 | 0.035712

                >> align_(ts0, ts1);                         % 2000Q1 -> 2001Q2
                >> ts0

                ts0 is a dseries object:

                       | Variable_1
                2000Q1 | 0.80028
                2000Q2 | 0.14189
                2000Q3 | 0.42176
                2000Q4 | 0.91574
                2001Q1 | 0.79221
                2001Q2 | NaN

                >> ts1

                ts1 is a dseries object:

                       | Variable_1
                2000Q1 | NaN
                2000Q2 | NaN
                2000Q3 | NaN
                2000Q4 | 0.95949
                2001Q1 | 0.65574
                2001Q2 | 0.035712


    .. dseriesmethod:: C = backcast (A, B[, diff])
                       backcast_ (A, B[, diff])

        Backcasts ``dseries`` object ``A`` with ``dseries`` object B's
        growth rates (except if the last optional argument, ``diff``,
        is true in which case first differences are used). Both
        ``dseries`` objects must have the same frequency.


    .. dseriesmethod:: B = baxter_king_filter (A[, hf[, lf[, K]]])
                       baxter_king_filter_ (A[, hf[, lf[, K]]])

        |br| Implementation of the *Baxter and King* (1999) band pass
        filter for ``dseries`` objects. This filter isolates business
        cycle fluctuations with a period of length ranging between
        ``hf`` (high frequency) to ``lf`` (low frequency) using a
        symmetric moving average smoother with :math:`2K+1` points, so
        that :math:`K` observations at the beginning and at the end of
        the sample are lost in the computation of the filter. The
        default value for ``hf`` is ``6``, for ``lf`` is ``32``, and
        for ``K`` is ``12``.

        *Example*

            ::

                % Simulate a component model (stochastic trend, deterministic
                % trend, and a stationary autoregressive process).
                e = 0.2*randn(200,1);
                u = randn(200,1);
                stochastic_trend = cumsum(e);
                deterministic_trend = .1*transpose(1:200);
                x = zeros(200,1);
                for i=2:200
                    x(i) = .75*x(i-1) + u(i);
                end
                y = x + stochastic_trend + deterministic_trend;

                % Instantiates time series objects.
                ts0 = dseries(y,'1950Q1');
                ts1 = dseries(x,'1950Q1'); % stationary component.

                % Apply the Baxter-King filter.
                ts2 = ts0.baxter_king_filter();

                % Plot the filtered time series.
                plot(ts1(ts2.dates).data,'-k'); % Plot of the stationary component.
                hold on
                plot(ts2.data,'--r');           % Plot of the filtered y.
                hold off
                axis tight
                id = get(gca,'XTick');
                set(gca,'XTickLabel',strings(ts1.dates(id)));


    .. dseriesmethod:: B = center (A[, geometric])
                       center_ (A[, geometric])

       |br| Centers variables in ``dseries`` object ``A`` around their
       arithmetic means, except if the optional argument ``geometric``
       is set equal to ``true`` in which case all the variables are
       divided by their geometric means.


    .. dseriesmethod:: C = chain (A, B)
                       chain_ (A, B)

        |br| Merge two ``dseries`` objects along the time
        dimension. The two objects must have the same number of
        observed variables, and the initial date in ``B`` must not be
        posterior to the last date in ``A``. The returned ``dseries``
        object, ``C``, is built by extending ``A`` with the cumulated
        growth factors of ``B``.

        *Example*

            ::

                >> ts = dseries([1; 2; 3; 4],dates('1950Q1'))

                ts is a dseries object:

                       | Variable_1
                1950Q1 | 1
                1950Q2 | 2
                1950Q3 | 3
                1950Q4 | 4

                >> us = dseries([3; 4; 5; 6],dates('1950Q3'))

                us is a dseries object:

                       | Variable_1
                1950Q3 | 3
                1950Q4 | 4
                1951Q1 | 5
                1951Q2 | 6

                >> chain(ts, us)

                ans is a dseries object:

                       | Variable_1
                1950Q1 | 1
                1950Q2 | 2
                1950Q3 | 3
                1950Q4 | 4
                1951Q1 | 5
                1951Q2 | 6

        *Example (in-place modification version)*

            ::

                >> ts = dseries([1; 2; 3; 4],dates('1950Q1'))
                >> us = dseries([3; 4; 5; 6],dates('1950Q3'))
                >> ts.chain_(us);
                >> ts

                ts is a dseries object:

                       | Variable_1
                1950Q1 | 1
                1950Q2 | 2
                1950Q3 | 3
                1950Q4 | 4
                1951Q1 | 5
                1951Q2 | 6


    .. dseriesmethod:: [error_flag, message ] = check (A)

        |br| Sanity check of ``dseries`` object ``A``. Returns ``1``
        if there is an error, ``0`` otherwise. The second output
        argument is a string giving brief informations about the
        error.


    .. dseriesmethod:: B = copy (A)

       |br| Returns a copy of ``A``. If an inplace modification method
       is applied to ``A``, object ``B`` will not be affected. Note
       that if ``A`` is assigned to ``C``, ``C = A``, then any in
       place modification method applied to ``A`` will change ``C``.

       *Example*

            ::

               >> a = dseries(randn(5,1))

               a is a dseries object:

                  | Variable_1
               1Y | -0.16936
               2Y | -1.1451
               3Y | -0.034331
               4Y | -0.089042
               5Y | -0.66997

               >> b = copy(a);
               >> c = a;
               >> a.abs();
               >> a.abs_();
               >> a

               a is a dseries object:

                  | Variable_1
               1Y | 0.16936
               2Y | 1.1451
               3Y | 0.034331
               4Y | 0.089042
               5Y | 0.66997

               >> b

               b is a dseries object:

                  | Variable_1
               1Y | -0.16936
               2Y | -1.1451
               3Y | -0.034331
               4Y | -0.089042
               5Y | -0.66997

               >> c

               c is a dseries object:

                  | Variable_1
               1Y | 0.16936
               2Y | 1.1451
               3Y | 0.034331
               4Y | 0.089042
               5Y | 0.66997


    .. dseriesmethod:: B = cumprod (A[, d[, v]])
                       cumprod_ (A[, d[, v]])

        |br| Overloads the MATLAB/Octave ``cumprod`` function for
        ``dseries`` objects. The cumulated product cannot be computed
        if the variables in ``dseries`` object ``A`` have NaNs. If a
        ``dates`` object ``d`` is provided as a second argument, then
        the method computes the cumulated product with the additional
        constraint that the variables in the ``dseries`` object ``B``
        are equal to one in period ``d``. If a single-observation
        ``dseries`` object ``v`` is provided as a third argument, the
        cumulated product in ``B`` is normalized such that ``B(d)``
        matches ``v`` (``dseries`` objects ``A`` and ``v`` must have
        the same number of variables).

        *Example*

            ::

                >> ts1 = dseries(2*ones(7,1));
                >> ts2 = ts1.cumprod();
                >> ts2

                ts2 is a dseries object:

                   | cumprod(Variable_1)
                1Y | 2
                2Y | 4
                3Y | 8
                4Y | 16
                5Y | 32
                6Y | 64
                7Y | 128

                >> ts3 = ts1.cumprod(dates('3Y'));
                >> ts3

                ts3 is a dseries object:

                   | cumprod(Variable_1)
                1Y | 0.25
                2Y | 0.5
                3Y | 1
                4Y | 2
                5Y | 4
                6Y | 8
                7Y | 16

                >> ts4 = ts1.cumprod(dates('3Y'),dseries(pi));
                >> ts4

                ts4 is a dseries object:

                   | cumprod(Variable_1)
                1Y | 0.7854
                2Y | 1.5708
                3Y | 3.1416
                4Y | 6.2832
                5Y | 12.5664
                6Y | 25.1327
                7Y | 50.2655


    .. dseriesmethod:: B = cumsum (A[, d[, v]])
                       cumsum_ (A[, d[, v]])

        |br| Overloads the MATLAB/Octave ``cumsum`` function for
        ``dseries`` objects. The cumulated sum cannot be computed if
        the variables in ``dseries`` object ``A`` have NaNs. If a
        ``dates`` object ``d`` is provided as a second argument, then
        the method computes the cumulated sum with the additional
        constraint that the variables in the ``dseries`` object ``B``
        are zero in period ``d``. If a single observation ``dseries``
        object ``v`` is provided as a third argument, the cumulated
        sum in ``B`` is such that ``B(d)`` matches ``v`` (``dseries``
        objects ``A`` and ``v`` must have the same number of
        variables).

        *Example*

            ::

                >> ts1 = dseries(ones(10,1));
                >> ts2 = ts1.cumsum();
                >> ts2

                ts2 is a dseries object:

                    | cumsum(Variable_1)
                1Y  | 1
                2Y  | 2
                3Y  | 3
                4Y  | 4
                5Y  | 5
                6Y  | 6
                7Y  | 7
                8Y  | 8
                9Y  | 9
                10Y | 10

                >> ts3 = ts1.cumsum(dates('3Y'));
                >> ts3

                ts3 is a dseries object:

                    | cumsum(Variable_1)
                1Y  | -2
                2Y  | -1
                3Y  | 0
                4Y  | 1
                5Y  | 2
                6Y  | 3
                7Y  | 4
                8Y  | 5
                9Y  | 6
                10Y | 7

                >> ts4 = ts1.cumsum(dates('3Y'),dseries(pi));
                >> ts4

                ts4 is a dseries object:

                    | cumsum(Variable_1)
                1Y  | 1.1416
                2Y  | 2.1416
                3Y  | 3.1416
                4Y  | 4.1416
                5Y  | 5.1416
                6Y  | 6.1416
                7Y  | 7.1416
                8Y  | 8.1416
                9Y  | 9.1416
                10Y | 10.1416


    .. dseriesmethod:: B = detrend (A[, m])
                       detrend_ (A[, m])

        |br| Detrends ``dseries`` object ``A`` with a fitted
        polynomial of order ``m``. Default value fir ``m`` is 0 (time
        series are detrended by removing the average). Note that each
        variable is detrended with a different polynomial.


    .. dseriesmethod:: B = dgrowth (A)
                       dgrowth_ (A)

        |br| Computes daily growth rates.


    .. dseriesmethod:: B = diff (A)
                       diff_ (A)

        |br| Returns the first difference of ``dseries`` object ``A``.


    .. datesmethod:: disp (A)

        |br| Overloads the MATLAB/Octave disp function for ``dseries`` object.


    .. datesmethod:: display (A)

        |br| Overloads the MATLAB/Octave display function for
        ``dseries`` object. ``display`` is the function called by
        MATLAB/Octave to print the content of an object if a semicolon is
        missing at the end of a MATLAB/Octave statement. If the ``dseries``
        object is defined over a too large time span, only the first
        and last periods will be printed. If the ``dseries`` object
        contains too many variables, only the first and last variables
        will be printed. If all the periods and variables are
        required, the ``disp`` method should be used instead.


    .. dseriesmethod:: C = eq (A, B)

        |br| Overloads the MATLAB/Octave ``eq`` (equal, ``==``)
        operator. ``dseries`` objects ``A`` and ``B`` must have the
        same number of observations (say, :math:`T`) and variables
        (:math:`N`). The returned argument is a :math:`T \times N`
        matrix of logicals. Element :math:`(i,j)` of ``C`` is
        equal to ``true`` if and only if observation :math:`i` for
        variable :math:`j` in ``A`` and ``B`` are the same.

        *Example*

            ::

                >> ts0 = dseries(2*ones(3,1));
                >> ts1 = dseries([2; 0; 2]);
                >> ts0==ts1

                ans =

                   3x1 logical array

                    1
                    0
                    1


    .. dseriesmethod:: l = exist (A, varname)

        |br| Tests if variable ``varname``  exists in ``dseries`` object ``A``. Returns
        ``true`` iff variable exists in ``A``.

        *Example*

            ::

                >> ts = dseries(randn(100,1));
                >> ts.exist('Variable_1')

                ans =

                   logical

                    1

                >> ts.exist('Variable_2')

                ans =

                   logical

                    0


    .. dseriesmethod:: B = exp (A)
                       exp_ (A)

        |br| Overloads the MATLAB/Octave ``exp`` function for
        ``dseries`` objects.

        *Example*

            ::

                >> ts0 = dseries(rand(10,1));
                >> ts1 = ts0.exp();

        *Exemple (in-place modification version)*

            ::

                >> ts0 = dseries(rand(3,1))

                ts0 is a dseries object:

                   | Variable_1
                1Y | 0.82953
                2Y | 0.84909
                3Y | 0.37253

                >> ts0.exp_();
                >> ts0

                ts0 is a dseries object:

                   | Variable_1
                1Y | 2.2922
                2Y | 2.3375
                3Y | 1.4514


    .. dseriesmethod:: C = extract (A, B[, ...])

        |br| Extracts some variables from a ``dseries`` object ``A``
        and returns a ``dseries`` object ``C``. The input arguments
        following ``A`` are strings representing the variables to be
        selected in the new ``dseries`` object ``C``. To simplify the
        creation of sub-objects, the ``dseries`` class overloads the
        curly braces (``D = extract (A, B, C)`` is equivalent to ``D =
        A{B,C}``) and allows implicit loops (defined between a pair of
        ``@`` symbol, see examples below) or MATLAB/Octave’s regular
        expressions (introduced by square brackets).

        *Example*

            The following selections are equivalent::

                >> ts0 = dseries(ones(100,10));
                >> ts1 = ts0{'Variable_1','Variable_2','Variable_3'};
                >> ts2 = ts0{'Variable_@1,2,3@'};
                >> ts3 = ts0{'Variable_[1-3]$'};
                >> isequal(ts1,ts2) && isequal(ts1,ts3)

                ans =

                   logical

                    1

            It is possible to use up to two implicit loops to select variables::

                names = {'GDP_1';'GDP_2';'GDP_3'; 'GDP_4'; 'GDP_5'; 'GDP_6'; 'GDP_7'; 'GDP_8'; ...
                    'GDP_9'; 'GDP_10'; 'GDP_11'; 'GDP_12'; ...
                    'HICP_1';'HICP_2';'HICP_3'; 'HICP_4'; 'HICP_5'; 'HICP_6'; 'HICP_7'; 'HICP_8'; ...
                    'HICP_9'; 'HICP_10'; 'HICP_11'; 'HICP_12'};

                ts0 = dseries(randn(4,24),dates('1973Q1'),names);
                ts0{'@GDP,HICP@_@1,3,5@'}

                ans is a dseries object:

                       | GDP_1    | GDP_3     | GDP_5     | HICP_1   | HICP_3   | HICP_5
                1973Q1 | 1.7906   | -1.6606   | -0.57716  | 0.60963  | -0.52335 | 0.26172
                1973Q2 | 2.1624   | 3.0125    | 0.52563   | 0.70912  | -1.7158  | 1.7792
                1973Q3 | -0.81928 | 1.5008    | 1.152     | 0.2798   | 0.88568  | 1.8927
                1973Q4 | -0.03705 | -0.35899  | 0.85838   | -1.4675  | -2.1666  | -0.62032


    .. dseriesmethod:: fill_(name, v)

       |br| Assign the value ``v`` to the variable ``name`` in a
       dseries object. If ``name`` is a character row array, it should
       correspond to an existing variable within the dseries
       object. When ``v`` is a scalar, its value will be applied to
       all periods uniformly. If ``v`` is a vector, its length must
       match the number of observations in the dseries object.You can
       invoke this method for a batch of variables by providing a 1 by
       n cell array of character row arrays as the first argument. When
       "v" is a row vector with n elements, the method will be applied
       uniformly across all periods. If "v" is a matrix, it must have
       n columns, and the number of rows should correspond to the
       number of periods.

       *Example*

            ::

                >> ts = dseries(rand(3,3));
                >> ts.fill_({'Variable_1', 'Variable_3'}, [1 3]);
                >> ts

                ts is a dseries object:

                   | Variable_1 | Variable_2 | Variable_3
                1Y | 1          | 0.91338    | 3
                2Y | 1          | 0.63236    | 3
                3Y | 1          | 0.09754    | 3


    .. dseriesmethod:: f = firstdate (A)

       |br| Returns the initial period in the ``dseries`` object ``A``.


    .. dseriesmethod:: f = firstobservedperiod (A)

       |br| Returns the first period where all the variables in ``dseries`` object ``A`` are observed (non NaN).


    .. dseriesmethod:: B = flip (A)
                       flip_ (A)

       |br| Flips the rows in the data member (without changing the
       periods order).


    .. dseriesmethod:: f = frequency (B)

        |br| Returns the frequency of the variables in ``dseries`` object ``B``.

        *Example*

            ::

                >> ts = dseries(randn(3,2),'1973Q1');
                >> ts.frequency

                ans =

                     4


    .. dseriesmethod:: l = ge (A, B)
                       l = gt (A, B)

       |br| Overloads the ``gt`` (>) and ``ge`` (>=) binary operators. Returns a logical array.

       *Example*

           ::

                >> ts = dseries(randn(3,1))

                ts is a dseries object:

                   | Variable_1
                1Y | -1.2075
                2Y | 0.71724
                3Y | 1.6302

                >> ts>1

                ans =

                  3x1 logical array

                   0
                   0
                   1

                >> ds = dseries(randn(3,1))

                ds is a dseries object:

                   | Variable_1
                1Y | 0.48889
                2Y | 1.0347
                3Y | 0.72689

                >> ds>ts

                ans =

                  3x1 logical array

                   1
                   1
                   0


    .. dseriesmethod:: B = hdiff (A)
                       hdiff_ (A)

       |br| Computes bi-annual differences.


    .. dseriesmethod:: B = hgrowth (A)
                       hgrowth_ (A)

       |br| Computes bi-annual growth rates.


   .. dseriesmethod:: D = horzcat (A, B[, ...])

        |br| Overloads the ``horzcat`` MATLAB/Octave’s method for
        ``dseries`` objects. Returns a ``dseries`` object ``D``
        containing the variables in ``dseries`` objects passed as
        inputs: ``A, B, ...`` If the inputs are not defined on the
        same time ranges, the method adds NaNs to the variables so
        that the variables are redefined on the smallest common time
        range. Note that the names in the ``dseries`` objects passed
        as inputs must be different and these objects must have common
        frequency.

        *Example*

            ::

                >> ts0 = dseries(rand(5,2),'1950Q1',{'nifnif';'noufnouf'});
                >> ts1 = dseries(rand(7,1),'1950Q3',{'nafnaf'});
                >> ts2 = [ts0, ts1];
                >> ts2

                ts2 is a dseries object:

                       | nifnif  | noufnouf | nafnaf
                1950Q1 | 0.17404 | 0.71431  | NaN
                1950Q2 | 0.62741 | 0.90704  | NaN
                1950Q3 | 0.84189 | 0.21854  | 0.83666
                1950Q4 | 0.51008 | 0.87096  | 0.8593
                1951Q1 | 0.16576 | 0.21184  | 0.52338
                1951Q2 | NaN     | NaN      | 0.47736
                1951Q3 | NaN     | NaN      | 0.88988
                1951Q4 | NaN     | NaN      | 0.065076
                1952Q1 | NaN     | NaN      | 0.50946


    .. dseriesmethod:: B = hpcycle (A[, lambda])
                       hpcycle_ (A[, lambda])

        |br| Extracts the cycle component from a ``dseries`` ``A``
        object using the *Hodrick and Prescott (1997)* filter and
        returns a ``dseries`` object, ``B``. The default value for
        ``lambda``, the smoothing parameter, is ``1600``.

        *Example*

            ::

                % Simulate a component model (stochastic trend, deterministic
                % trend, and a stationary autoregressive process).
                e = 0.2*randn(200,1);
                u = randn(200,1);
                stochastic_trend = cumsum(e);
                deterministic_trend = .1*transpose(1:200);
                x = zeros(200,1);
                for i=2:200
                    x(i) = .75*x(i-1) + u(i);
                end
                y = x + stochastic_trend + deterministic_trend;

                % Instantiates time series objects.
                ts0 = dseries(y,'1950Q1');
                ts1 = dseries(x,'1950Q1'); % stationary component.

                % Apply the HP filter.
                ts2 = ts0.hpcycle();

                % Plot the filtered time series.
                plot(ts1(ts2.dates).data,'-k'); % Plot of the stationary component.
                hold on
                plot(ts2.data,'--r');           % Plot of the filtered y.
                hold off
                axis tight
                id = get(gca,'XTick');
                set(gca,'XTickLabel',strings(ts.dates(id)));


    .. dseriesmethod:: B = hptrend (A[, lambda])
                       hptrend_ (A[, lambda])

        |br| Extracts the trend component from a ``dseries`` A object
        using the *Hodrick and Prescott (1997)* filter and returns a
        ``dseries`` object, ``B``. Default value for ``lambda``, the
        smoothing parameter, is ``1600``.

        *Example*

            ::

                % Using the same generating data process
                % as in the previous example:

                ts1 = dseries(stochastic_trend + deterministic_trend,'1950Q1');
                % Apply the HP filter.
                ts2 = ts0.hptrend();

                % Plot the filtered time series.
                plot(ts1.data,'-k'); % Plot of the nonstationary components.
                hold on
                plot(ts2.data,'--r');  % Plot of the estimated trend.
                hold off
                axis tight
                id = get(gca,'XTick');
                set(gca,'XTickLabel',strings(ts0.dates(id)));


    .. dseriesmethod:: C = insert (A, B, I)

        |br| Inserts variables contained in ``dseries`` object ``B``
        in ``dseries`` object ``A`` at positions specified by integer
        scalars in vector ``I``, returns augmented ``dseries`` object
        ``C``. The integer scalars in ``I`` must take values between
        `` and ``A.length()+1`` and refers to ``A`` ’s column
        numbers. The ``dseries`` objects ``A`` and ``B`` need not be
        defined over the same time ranges, but it is assumed that they
        have common frequency.

        *Example*

            ::

                >> ts0 = dseries(ones(2,4),'1950Q1',{'Sly'; 'Gobbo'; 'Sneaky'; 'Stealthy'});
                >> ts1 = dseries(pi*ones(2,1),'1950Q1',{'Noddy'});
                >> ts2 = ts0.insert(ts1,3)

                ts2 is a dseries object:

                       | Sly | Gobbo | Noddy  | Sneaky | Stealthy
                1950Q1 | 1   | 1     | 3.1416 | 1      | 1
                1950Q2 | 1   | 1     | 3.1416 | 1      | 1

                >> ts3 = dseries([pi*ones(2,1) sqrt(pi)*ones(2,1)],'1950Q1',{'Noddy';'Tessie Bear'});
                >> ts4 = ts0.insert(ts1,[3, 4])

                ts4 is a dseries object:

                       | Sly | Gobbo | Noddy  | Sneaky | Tessie Bear | Stealthy
                1950Q1 | 1   | 1     | 3.1416 | 1      | 1.7725      | 1
                1950Q2 | 1   | 1     | 3.1416 | 1      | 1.7725      | 1


    .. dseriesmethod:: B = isempty (A)

       |br| Overloads the MATLAB/Octave’s ``isempty`` function. Returns
       ``true`` if ``dseries`` object ``A`` is empty.


    .. dseriesmethod:: C = isequal (A, B)

        |br| Overloads the MATLAB/Octave’s ``isequal`` function. Returns
        ``true`` if ``dseries`` objects ``A`` and ``B`` are identical.


    .. dseriesmethod:: C = isinf (A)

        |br| Overloads the MATLAB/Octave’s ``isinf`` function. Returns
        a logical array, with element ``(i,j)`` equal to ``true`` if and
        only if variable ``j`` is finite in period ``A.dates(i)``.


    .. dseriesmethod:: C = isnan (A)

        |br| Overloads the MATLAB/Octave’s ``isnan`` function. Returns
        a logical array, with element ``(i,j)`` equal to ``true`` if and
        only if variable ``j`` isn't NaN in period ``A.dates(i)``.


    .. dseriesmethod:: C = isreal (A)

        |br| Overloads the MATLAB/Octave’s ``isreal`` function. Returns
        a logical array, with element ``(i,j)`` equal to ``true`` if and
        only if variable ``j`` is real in period ``A.dates(i)``.


    .. dseriesmethod:: B = lag (A[, p])
                       lag_ (A[, p])

        |br| Returns lagged time series. Default value of integer
        scalar ``p``, the number of lags, is ``1``. The `dseries`
        class overloads the parentheses, so that `ts.lag(p)` is
        equivalent to `ts(-p)`.

        *Example*

            ::

                >> ts0 = dseries(transpose(1:4), '1950Q1')

                ts0 is a dseries object:

                       | Variable_1
                1950Q1 | 1
                1950Q2 | 2
                1950Q3 | 3
                1950Q4 | 4

                >> ts1 = ts0.lag()

                ts1 is a dseries object:

                           | Variable_1
                    1950Q1 | NaN
                    1950Q2 | 1
                    1950Q3 | 2
                    1950Q4 | 3

                >> ts2 = ts0.lag(2)

                ts2 is a dseries object:

                       | Variable_1
                1950Q1 | NaN
                1950Q2 | NaN
                1950Q3 | 1
                1950Q4 | 2

                % dseries class overloads the parenthesis
                % so that ts.lag(p) can be written more
                % compactly as ts(-p). For instance:

                >> ts0.lag(1)

                ans is a dseries object:

                       | Variable_1
                1950Q1 | NaN
                1950Q2 | 1
                1950Q3 | 2
                1950Q4 | 3

            or alternatively::

                >> ts0(-1)

                ans is a dseries object:

                       | Variable_1
                1950Q1 | NaN
                1950Q2 | 1
                1950Q3 | 2
                1950Q4 | 3


    .. dseriesmethod:: l = lastdate (B)

        |br| Retrieves the final period from the ``dseries`` object ``B``.

        *Example*

            ::

                >> ts = dseries(randn(3,2),'1973Q1');
                >> ts.lastdate()

                ans = <dates: 1973Q3>


    .. dseriesmethod:: f = lastobservedperiod (A)

       |br| Returns the last period in which all variables of the
       ``dseries`` object ``A`` are fully observed (i.e., contain no
       NaN values).


    .. dseriesmethod:: f = lastobservedperiods (A)

       |br| Returns the last period without missing observations for
       each variable in the ``dseries`` object ``A``. The output
       argument ``f`` is a structure where each field name corresponds
       to a variable in ``A``, and the content of each field is a
       singleton ``date`` object.


    .. dseriesmethod:: l = le (A, B)
                       l = lt (A, B)

       |br| Overloads the ``gt`` (<) and ``ge`` (<=) binary operators. Returns a logical array.

       *Example*

           ::

                >> ts = dseries(randn(3,1))

                ts is a dseries object:

                   | Variable_1
                1Y | -1.2075
                2Y | 0.71724
                3Y | 1.6302

                >> ts<1

                ans =

                  3x1 logical array

                   1
                   1
                   0

                >> ds = dseries(randn(3,1))

                ds is a dseries object:

                   | Variable_1
                1Y | 0.48889
                2Y | 1.0347
                3Y | 0.72689

                >> ds<ts

                ans =

                  3x1 logical array

                   0
                   0
                   1


    .. dseriesmethod:: B = lead (A[, p])
                       lead_ (A[, p])

        |br| Returns a lead time series. The default value for the
        integer scalar ``p``, which represents the number of leads, is
        ``1``. Similar to the ``lag`` method, the ``dseries`` class
        overloads the parentheses, making ``ts.lead(p)`` equivalent to
        ``ts(p)``.

        *Example*

            ::

                >> ts0 = dseries(transpose(1:4),'1950Q1');
                >> ts1 = ts0.lead()

                ts1 is a dseries object:

                       | Variable_1
                1950Q1 | 2
                1950Q2 | 3
                1950Q3 | 4
                1950Q4 | NaN

                >> ts2 = ts0(2)

                ts2 is a dseries object:

                       | Variable_1
                1950Q1 | 3
                1950Q2 | 4
                1950Q3 | NaN
                1950Q4 | NaN

        *Remark*

        The overload of parentheses for ``dseries`` objects simplifies
        the creation of new ``dseries`` instances by enabling the
        direct copying and pasting of equations defined within the
        ``model`` block. For example, if an Euler equation is
        specified in the ``model`` block,::

            model;
            ...
            1/C - beta/C(1)*(exp(A(1))*K^(alpha-1)+1-delta) ;
            ...
            end;

        and if variables ``, ``A`` and ``K`` are defined as
        ``dseries`` objects, then by writing::

            Residuals = 1/C - beta/C(1)*(exp(A(1))*K^(alpha-1)+1-delta) ;

        outside of the ``model`` block, we create a new ``dseries``
        object, called ``Residuals``, for the residuals of the Euler
        equation (the conditional expectation of the equation defined
        in the ``model`` block is zero, but the residuals are non
        zero).


    .. dseriesmethod:: B = lineartrend (A)

        |br| Returns a linear trend centered on 0, the length of the
        trend is given by the size of ``dseries`` object ``A`` (the
        number of periods).

        *Example*

            ::

               >> ts = dseries(ones(3,1));
               >> ts.lineartrend()

               ans =

                    -1
                     0
                     1


    .. dseriesmethod:: B = log (A)
                       log_ (A)

        |br| Overloads the MATLAB/Octave ``log`` function for
        ``dseries`` objects.

        *Example*

            ::

                >> ts0 = dseries(rand(10,1));
                >> ts1 = ts0.log();

    .. dseriesmethod:: B = mdiff (A)
                       mdiff_ (A)
                       B = mgrowth (A)
                       mgrowth_ (A)

       |br| Calculates the monthly differences or growth rates of
       variables in the ``dseries`` object ``A``.


    .. dseriesmethod:: B = mean (A[, geometric])

        |br| This function overloads the MATLAB/Octave ``mean``
        function specifically for ``dseries`` objects. It calculates
        the mean for each variable within the ``dseries`` object
        ``A``. If the second argument is set to ``true``, the
        geometric mean is calculated; otherwise, the arithmetic mean
        is computed by default.


    .. dseriesmethod:: C = merge (A, B[, legacy])

        |br| Merges two ``dseries`` objects, ``A`` and ``B``, into a new
        ``dseries`` object ``C``. The objects ``A`` and ``B`` must share a
        common frequency, although they can cover different time
        ranges. If a variable, such as ``x``, exists in both ``dseries``
        objects, the ``merge`` function will prioritize the definition
        from the second input, ``B``, while retaining the values from
        ``A`` for any corresponding periods where ``B`` has NaN
        values. This behavior can be altered by setting the optional
        argument ``legacy`` to true, in which case the second variable
        will replace the first, even if it contains NaN values.

        *Example*

            ::

               >> ts0 = dseries(rand(3,2),'1950Q1',{'A1';'A2'})

               ts0 is a dseries object:

                      | A1      | A2
               1950Q1 | 0.96284 | 0.5363
               1950Q2 | 0.25145 | 0.31866
               1950Q3 | 0.34447 | 0.4355

               >> ts1 = dseries(rand(3,1),'1950Q2',{'A1'})

               ts1 is a dseries object:

                      | A1
               1950Q2 | 0.40161
               1950Q3 | 0.81763
               1950Q4 | 0.97769

               >> merge(ts0,ts1)

               ans is a dseries object:

                      | A1      | A2
               1950Q1 | 0.96284 | 0.5363
               1950Q2 | 0.40161 | 0.31866
               1950Q3 | 0.81763 | 0.4355
               1950Q4 | 0.97769 | NaN

                >> merge(ts1,ts0)

                ans is a dseries object:

                      | A1      | A2
               1950Q1 | 0.96284 | 0.5363
               1950Q2 | 0.25145 | 0.31866
               1950Q3 | 0.34447 | 0.4355
               1950Q4 | 0.97769 | NaN


    .. dseriesmethod:: C = minus (A, B)

        |br| Overloads the MATLAB/Octave ``minus`` (``-``) operator
        for ``dseries`` objects, allowing for element-by-element
        subtraction. When both ``A`` and ``B`` are ``dseries``
        objects, they do not need to be defined over the same time
        ranges. If ``A`` and ``B`` have :math:`T_A` and :math:`T_B`
        observations and :math:`N_A` and :math:`N_B` variables, then
        :math:`N_A` must equal :math:`N_B` or :math:`1`, and
        :math:`N_B` must equal :math:`N_A` or :math:`1`. If
        :math:`T_A=T_B`, ``isequal(A.init,B.init)`` returns ``1``,
        and :math:`N_A=N_B`, then the ``minus`` operator will compute
        for each pair :math:`(t,n)`, where :math:`1\le t\le T_A` and
        :math:`1\le n\le N_A`, the operation
        ``C.data(t,n)=A.data(t,n)-B.data(t,n)``. If :math:`N_B` equals
        :math:`1` and :math:`N_A>1`, the smaller ``dseries`` object
        (``B``) is “broadcasted” across the larger ``dseries`` (``A``),
        ensuring compatible shapes for the subtraction of the variable
        defined in ``B`` from each variable in ``A``. If ``B`` is a
        double scalar, the ``minus`` method will subtract ``B`` from
        all observations and variables in ``A``. If ``B`` is a row
        vector of length :math:`N_A`, the ``minus`` method will
        subtract ``B(i)`` from all observations of variable ``i``, for
        :math:`i=1,...,N_A`. If ``B`` is a column vector of length
        :math:`T_A`, the ``minus`` method will subtract ``B`` from all
        the variables.

        *Example*

            ::

                >> ts0 = dseries(rand(3,2));
                >> ts1 = ts0{'Variable_2'};
                >> ts0-ts1

                ans is a dseries object:

                   | Variable_1 | Variable_2
                1Y | -0.48853   | 0
                2Y | -0.50535   | 0
                3Y | -0.32063   | 0

                >> ts1

                ts1 is a dseries object:

                   | Variable_2
                1Y | 0.703
                2Y | 0.75415
                3Y | 0.54729

                >> ts1-ts1.data(1)

                ans is a dseries object:

                   | Variable_2
                1Y | 0
                2Y | 0.051148
                3Y | -0.15572

                >> ts1.data(1)-ts1

                ans is a dseries object:

                   | Variable_2
                1Y | 0
                2Y | -0.051148
                3Y | 0.15572


    .. dseriesmethod:: C = mpower (A, B)

        |br| Overloads the MATLAB/Octave ``mpower`` (``^``) operator
        for ``dseries`` objects, performing element-wise
        exponentiation. Given a ``dseries`` object ``A`` with ``N``
        variables and ``T`` observations, if ``B`` is a real scalar,
        then ``mpower(A,B)`` yields a ``dseries`` object ``C`` where
        ``C.data(t,n) = A.data(t,n)^B``. If ``B`` is also a
        ``dseries`` object with ``N`` variables and ``T``
        observations, then ``mpower(A,B)`` produces a ``dseries``
        object ``C`` such that ``C.data(t,n) =
        A.data(t,n)^{C.data(t,n)}``.

        *Example*

            ::

                >> ts0 = dseries(transpose(1:3));
                >> ts1 = ts0^2

                ts1 is a dseries object:

                   | Variable_1
                1Y | 1
                2Y | 4
                3Y | 9

                >> ts2 = ts0^ts0

                ts2 is a dseries object:

                   | Variable_1
                1Y | 1
                2Y | 4
                3Y | 27


    .. dseriesmethod:: C = mrdivide (A, B)

        |br| Overloads the MATLAB/Octave ``mrdivide`` (``/``) operator
        for ``dseries`` objects, enabling element-wise division
        similar to the ``./`` operator in MATLAB/Octave. When both
        ``A`` and ``B`` are ``dseries`` objects, they can have
        different time ranges. If ``A`` contains :math:`T_A`
        observations and :math:`N_A` variables, and ``B`` has
        :math:`T_B` observations and :math:`N_B` variables, then
        :math:`N_A` must equal :math:`N_B` or :math:`1`, and vice
        versa. If :math:`T_A=T_B` and ``isequal(A.init,B.init)``
        returns ``1``, along with :math:`N_A=N_B`, the ``mrdivide``
        operator calculates for each pair :math:`(t,n)`, where
        :math:`1\le t\le T_A` and :math:`1\le n\le N_A`, the value of
        ``C.data(t,n)=A.data(t,n)/B.data(t,n)``. If :math:`N_B` equals
        :math:`1` and :math:`N_A>1`, the smaller ``dseries`` object
        (``B``) is “broadcast” across the larger one (``A``) to ensure
        compatible shapes. In this case, the ``mrdivide`` operator
        divides each variable in ``A`` by the variable in ``B``,
        observation by observation. If ``B`` is a double scalar, then
        ``mrdivide`` will divide all observations and variables in
        ``A`` by ``B``. If ``B`` is a row vector of length
        :math:`N_A`, then ``mrdivide`` will divide each observation of
        variable ``i`` by ``B(i)``, for :math:`i=1,...,N_A`. If ``B``
        is a column vector of length :math:`T_A`, then ``mrdivide``
        will perform an element-wise division of all variables by
        ``B``.

        *Example*

            ::

                >> ts0 = dseries(rand(3,2))

                ts0 is a dseries object:

                   | Variable_1 | Variable_2
                1Y | 0.72918    | 0.90307
                2Y | 0.93756    | 0.21819
                3Y | 0.51725    | 0.87322

                >> ts1 = ts0{'Variable_2'};
                >> ts0/ts1

                ans is a dseries object:

                   | Variable_1 | Variable_2
                1Y | 0.80745    | 1
                2Y | 4.2969     | 1
                3Y | 0.59235    | 1


    .. dseriesmethod:: C = mtimes (A, B)

        |br| Overloads the MATLAB/Octave ``mtimes`` (``*``) operator
        for ``dseries`` objects, enabling element-wise multiplication
        similar to the ``.*`` operator in MATLAB/Octave. When both
        ``A`` and ``B`` are ``dseries`` objects, they can have
        different time ranges. If ``A`` contains :math:`T_A`
        observations and :math:`N_A` variables, and ``B`` has
        :math:`T_B` observations and :math:`N_B` variables, then
        :math:`N_A` must equal :math:`N_B` or :math:`1`, and vice
        versa. If :math:`T_A=T_B` and ``isequal(A.init,B.init)``
        returns ``1``, along with :math:`N_A=N_B`, the ``mtimes``
        operator calculates for each pair :math:`(t,n)`, where
        :math:`1\le t\le T_A` and :math:`1\le n\le N_A`, the value of
        ``C.data(t,n)=A.data(t,n)*B.data(t,n)``. If :math:`N_B` equals
        :math:`1` and :math:`N_A>1`, the smaller ``dseries`` object
        (``B``) is “broadcasted” across the larger one (``A``) to ensure
        compatible shapes. In this case, the ``mtimes`` operator
        multiply each variable in ``A`` by the variable in ``B``,
        observation by observation. If ``B`` is a double scalar, then
        ``mtimes`` will multiply all observations and variables in
        ``A`` by ``B``. If ``B`` is a row vector of length
        :math:`N_A`, then ``mtimes`` will multiply each observation of
        variable ``i`` by ``B(i)``, for :math:`i=1,...,N_A`. If ``B``
        is a column vector of length :math:`T_A`, then ``mtimes``
        will perform an element-wise multiplication of all variables by
        ``B``.


    .. dseriesmethod:: B = nanmean (A[, geometric])

        |br| Overloads the MATLAB/Octave ``nanmean`` function for
        ``dseries`` objects. Computes the mean of each variable in the
        ``dseries`` object ``A``, excluding NaN values. If the second
        argument is ``true``, the geometric mean is calculated;
        otherwise, the default is to report the arithmetic mean.


    .. dseriesmethod:: B = nanstd (A[, geometric])

        |br| Overloads the MATLAB/Octave ``nanstd`` function for
        ``dseries`` objects. This function calculates the standard
        deviation for each variable within the ``dseries`` object
        ``A``, while disregarding any NaN values. If the second
        argument is set to ``true``, the geometric standard deviation
        will be computed; the default value for the second argument is
        ``false``.


    .. dseriesmethod:: C = ne (A, B)

        |br| Overloads the MATLAB/Octave ``ne`` (not equal, ``~=``)
        operator. The ``dseries`` objects ``A`` and ``B`` must contain
        the same number of observations (denoted as :math:`T`) and
        variables (denoted as :math:`N`). The output is a :math:`T` by
        :math:`N` matrix consisting of zeros and ones. The element
        :math:`(i,j)` of the matrix ``C`` is equal to ``1`` if and
        only if observation :math:`i` for variable :math:`j` in ``A``
        and ``B`` are not equal.

        *Example*

            ::

                >> ts0 = dseries(2*ones(3,1));
                >> ts1 = dseries([2; 0; 2]);
                >> ts0~=ts1

                ans =

                  3x1 logical array

                   0
                   1
                   0


    .. dseriesmethod:: B = nobs (A)

        |br| Returns the number of observations in ``dseries`` object
        ``A``.

        *Example*

            ::

                >> ts0 = dseries(randn(10));
                >> ts0.nobs

                ans =

                    10


    .. dseriesmethod:: B = onesidedhpcycle (A[, lambda[, init]])
                       onesidedhpcycle_ (A[, lambda[, init]])

        |br| Extracts the cycle component from a ``dseries`` ``A``
        object using a one-sided HP filter (implemented with a Kalman
        filter) and returns a ``dseries`` object, ``B``. The default
        value for ``lambda``, the smoothing parameter, is set to
        ``1600``. By default, if ``init`` is not provided, the initial
        value is determined from the first two observations.


    .. dseriesmethod:: B = onesidedhptrend (A[, lambda[, init]])
                       onesidedhptrend_ (A[, lambda[, init]])

        |br| Extracts the trend component from a ``dseries`` ``A``
        object using a one-sided HP filter (implemented with a Kalman
        filter) and returns a ``dseries`` object, ``B``. The default
        value for ``lambda``, the smoothing parameter, is set to
        ``1600``. By default, if ``init`` is not provided, the initial
        value is derived from the first two observations.


    .. dseriesmethod:: h = plot (A)
                       h = plot (A, B)
                       h = plot (A[, ...])
                       h = plot (A, B[, ...])

        |br| Overloads the MATLAB/Octave ``plot`` function for
        ``dseries`` objects. This function returns a MATLAB/Octave
        plot handle, which can be utilized to modify the properties of
        the plotted time series. If a single ``dseries`` object,
        ``A``, is provided as an argument, the plot function will
        place the corresponding dates on the x-axis. If this
        ``dseries`` object contains only one variable, additional
        arguments can be included to adjust the plot properties,
        similar to how one would with MATLAB/Octave's original plot
        function. However, if the ``dseries`` object ``A`` has more
        than one variable, additional arguments cannot be passed, and
        modifications to the plotted time series properties must be
        done using the returned plot handle alongside the
        MATLAB/Octave ``set`` function (refer to the example
        below). When two ``dseries`` objects, ``A`` and ``B``, are
        passed as input arguments, the plot function will display the
        variables in ``A`` against those in ``B`` (it is essential
        that both objects contain the same number of variables;
        otherwise, an error will occur). Once more, if each object
        includes only one variable, additional arguments can be
        utilized to alter the plotted time series properties;
        otherwise, the MATLAB/Octave ``set`` command must be employed.

        *Example*

            Define a ``dseries`` object with two variables (named by
            default ``Variable_1`` and ``Variable_2``)::

                >> ts = dseries(randn(100,2),'1950Q1');

            The following command will plot the first variable in ``ts``::

                >> plot(ts{'Variable_1'},'-k','linewidth',2);

            The next command will draw all the variables in ``ts`` on
            the same figure::

                >> h = plot(ts);

            If one wants to modify the properties of the plotted time
            series (line style, colours, ...), the set function can be
            used (see MATLAB/Octave’s documentation)::

                >> set(h(1),'-k','linewidth',2);
                >> set(h(2),'--r');

            The following command will plot ``Variable_1`` against
            ``exp(Variable_1)``::

                >> plot(ts{'Variable_1'},ts{'Variable_1'}.exp(),'ok');

            Again, the properties can also be modified using the
            returned plot handle and the ``set`` function::

                >> h = plot(ts, ts.exp());
                >> set(h(1),'ok');
                >> set(h(2),'+r');


    .. dseriesmethod:: C = plus (A, B)

        |br| Overloads the MATLAB/Octave ``plus`` (``+``) operator for
        ``dseries`` objects, allowing for element-wise addition. When both
        ``A`` and ``B`` are ``dseries`` objects, they do not need to
        be defined over the same time ranges. If ``A`` and ``B`` are
        ``dseries`` objects with :math:`T_A` and :math:`T_B`
        observations and :math:`N_A` and :math:`N_B` variables, then
        :math:`N_A` must be equal to :math:`N_B` or :math:`1` and
        :math:`N_B` must be equal to :math:`N_A` or :math:`1`. If
        :math:`T_A=T_B`, ``isequal(A.init,B.init)`` returns ``1`` and
        :math:`N_A=N_B`, then the ``plus`` operator will compute for
        each pair :math:`(t,n)`, with :math:`1\le t\le T_A` and
        :math:`1\le n\le N_A`,
        ``C.data(t,n)=A.data(t,n)+B.data(t,n)``. If :math:`N_B` is
        equal to :math:`1` and :math:`N_A>1`, the smaller ``dseries``
        object (``B``) is “broadcasted” across the larger ``dseries``
        (``A``) to ensure compatible shapes, the plus operator
        will add the variable defined in ``B`` to each variable in
        ``A``. If ``B`` is a double scalar, then the method ``plus``
        will add ``B`` to all the observations/variables in ``A``. If
        ``B`` is a row vector of length :math:`N_A`, then the ``plus``
        method will add ``B(i)`` to all the observations of variable
        ``i``, for :math:`i=1,\ldots,N_A`. If ``B`` is a column vector of
        length :math:`T_A`, then the ``plus`` method will add ``B`` to
        all the variables.


    .. dseriesmethod:: C = pop (A[, B])
                       pop_ (A[, B])

        |br| Removes the variable ``B`` from the ``dseries`` object
        ``A``. By default, if the second argument is not specified, the
        last variable is removed.

        *Example*

            ::

                >> ts0 = dseries(ones(3,3));
                >> ts1 = ts0.pop('Variable_2');

                ts1 is a dseries object:

                   | Variable_1 | Variable_3
                1Y | 1          | 1
                2Y | 1          | 1
                3Y | 1          | 1


    .. dseriesmethod:: A = projection (A, info, periods)

        |br| Projects variables in the dseries object ``A``. The
        ``info`` variable is a :math:`n \times 3` cell array, where
        each row contains essential information for projecting a
        variable. The first column holds the variable name (as a
        character array), while the second column indicates the
        projection method used (also a character array). The possible
        values for this column are ``'Trend'``, ``'Constant'``, and
        ``'AR'``. The third column provides quantitative details
        related to the projection: if the second column is
        ``'Trend'``, the third column specifies the growth factor of
        the (exponential) trend; if ``'Constant'``, it indicates the
        variable's level; and if ``'AR'``, it denotes the
        autoregressive parameter. Variables can be projected using an
        AR(p) model if the third column contains a 1×p vector of
        doubles. Note that the stationarity of the AR(p) model is not
        tested. For constant projections, one can use either `'Trend'`
        with a growth factor of 1 or `'AR'` with an autoregressive
        parameter of one (indicating a random walk). This projection
        routine solely addresses exponential trends.

        *Example*

            ::

                >> data = ones(10,4);
                >> ts = dseries(data, '1990Q1', {'A1', 'A2', 'A3', 'A4'});
                >> info = {'A1', 'Trend', 1.2; 'A2', 'Constant', 0.0; 'A3', 'AR', .5; 'A4', 'AR', [.4, -.2]};
                >> ts.projection(info, 10);


    .. dseriesmethod:: B = qdiff (A)
                       B = qgrowth (A)
                       qdiff_ (A)
                       qgrowth_ (A)

        |br| Computes quarterly differences or growth rates.

        *Example*

            ::

                >> ts0 = dseries(transpose(1:4),'1950Q1');
                >> ts1 = ts0.qdiff()

                ts1 is a dseries object:

                       | Variable_1
                1950Q1 | NaN
                1950Q2 | 1
                1950Q3 | 1
                1950Q4 | 1

                >> ts0 = dseries(transpose(1:6),'1950M1');
                >> ts1 = ts0.qdiff()

                ts1 is a dseries object:

                        | Variable_1
                1950M1  | NaN
                1950M2  | NaN
                1950M3  | NaN
                1950M4  | 3
                1950M5  | 3
                1950M6  | 3


    .. dseriesmethod:: C = remove (A, B)
                       remove_ (A, B)

        |br| If ``B`` is a row character array representing the name
        of a variable, these methods serve as aliases for the ``pop``
        and ``pop_`` methods that accept two arguments. They remove
        the variable ``B`` from the ``dseries`` object ``A``. To
        remove multiple variables, you can pass a cell array of row
        character arrays for ``B``.

        *Example*

            ::

                >> ts0 = dseries(ones(3,3));
                >> ts1 = ts0.remove('Variable_2');

                ts1 is a dseries object:

                   | Variable_1 | Variable_3
                1Y | 1          | 1
                2Y | 1          | 1
                3Y | 1          | 1

            A more concise syntax is available: ``remove(ts,
            'Variable_2')``, which is equivalent to ``ts{'Variable_2'}
            = []`` (where ``[]`` can be substituted with any empty
            object). This alternative syntax proves useful when
            removing multiple variables. For example::

                ts{'Variable_@2,3,4@'} = [];

            will remove ``Variable_2``, ``Variable_3`` and
            ``Variable_4`` from ``dseries`` object ``ts`` (if these
            variables exist). Regular expressions cannot be used but
            implicit loops can.


    .. dseriesmethod:: B = rename (A, oldname, newname)
                       rename_ (A, oldname, newname)

        |br| Renames the variable ``oldname`` to ``newname`` in the
        ``dseries`` object ``A``. This function returns a ``dseries``
        object. If multiple variables need to be renamed, you can
        provide cell arrays of row character arrays as the second and
        third arguments.

        *Example*

            ::

                >> ts0 = dseries(ones(2,2));
                >> ts1 = ts0.rename('Variable_1','Stinkly')

                ts1 is a dseries object:

                   | Stinkly | Variable_2
                1Y | 1       | 1
                2Y | 1       | 1


    .. dseriesmethod:: C = rename (A, newname)
                       rename_ (A, newname)

        |br| Replace the names in ``A`` with those specified in the
        cell of row character arrays ``newname``. The cell ``newname`` must contain
        the same number of elements as there are variables in the
        ``dseries`` object ``A``.

        *Example*

            ::

                >> ts0 = dseries(ones(2,3));
                >> ts1 = ts0.rename({'TinkyWinky','Dipsy','LaaLaa'})

                ts1 is a dseries object:

                   | TinkyWinky | Dipsy | LaaLaa
                1Y | 1          | 1     | 1
                2Y | 1          | 1     | 1


    .. dseriesmethod:: A = resetops (A, ops)

        |br| Redefine ``ops`` member.


    .. dseriesmethod:: A = resetags (A, ops)

        |br| Redefine ``tags`` member.


    .. dseriesmethod:: B = round (A[, n])
                       round_ (A[, n])

        |br| Rounds each value to the nearest decimal or integer. The
        parameter ``n`` specifies the precision (number of decimal
        places), with a default value of 0, indicating that the method
        will round to the nearest integer by default.

        *Example*

            ::

                >> ts = dseries(pi)

                ts is a dseries object:

                   | Variable_1
                1Y | 3.1416

                >> ts.round_();
                >> ts

                ts is a dseries object:

                   | Variable_1
                1Y | 3


    .. dseriesmethod:: save (A, basename[, format])

        |br| Overloads the MATLAB/Octave ``save`` function to save the
        ``dseries`` object ``A`` to disk. The available formats
        include ``mat`` (default, MATLAB/Octave binary data file), ``m``
        (MATLAB/Octave script), and ``csv`` (comma-separated values
        file). The base name of the file, excluding the extension, is
        specified by ``basename``.

        *Example*

            ::

                >> ts0 = dseries(ones(2,2));
                >> ts0.save('ts0', 'csv');

            The last command will create a file ts0.csv with the
            following content::

                ,Variable_1,Variable_2
                1Y,               1,               1
                2Y,               1,               1

            To create a MATLAB/Octave script, the following command::

                >> ts0.save('ts0','m');

            will produce a file ts0.m with the following content::

                % File created on 14-Nov-2013 12:08:52.

                FREQ__ = 1;
                INIT__ = ' 1Y';

                NAMES__ = {'Variable_1'; 'Variable_2'};
                TEX__ = {'Variable_{1}'; 'Variable_{2}'};
                OPS__ = {};
                TAGS__ = struct();

                Variable_1 = [
                              1
                              1];

                Variable_2 = [
                              1
                              1];

            The generated (``csv``, ``m``, or ``mat``) files can be
            loaded when instantiating a ``dseries`` object as
            explained above.


    .. dseriesmethod:: B = set_names(A, s1, s2, ...)

        |br| Renames the variables in the ``dseries`` object ``A`` and
        returns a new ``dseries`` object ``B`` with the updated names
        ``s1``, ``s2``, and so forth. The number of input arguments
        following the first one (the ``dseries`` object ``A``) must be
        equal to ``A.vobs`` (the total number of variables in
        ``A``). The name ``s1`` will correspond to the first variable
        in ``B``, ``s2`` to the second variable in ``B``, and this
        pattern continues for the remaining variables.

        *Example*

            ::

                >> ts0 = dseries(ones(1,3));
                >> ts1 = ts0.set_names('Barbibul',[],'Barbouille')

                ts1 is a dseries object:

                   | Barbibul | Variable_2 | Barbouille
                1Y | 1        | 1          | 1


    .. dseriesmethod:: [T, N ] = size(A[, dim])

        Overloads the MATLAB/Octave ``size`` function to return the
        number of observations in the ``dseries`` object ``A`` (i.e.,
        ``A.nobs``) as well as the number of variables (i.e.,
        ``A.vobs``). If a second input argument is provided, the
        ``size`` function will return the number of observations when
        ``dim=1`` or the number of variables when ``dim=2``. An error
        will be issued for any other values of ``dim``.

        *Example*

            ::

                >> ts0 = dseries(ones(1,3));
                >> ts0.size()

                ans =

                     1     3


    .. dseriesmethod:: B = std (A[, geometric])

        |br| Overloads the MATLAB/Octave ``std`` function for
        ``dseries`` objects. This function returns the standard
        deviation of each variable within the ``dseries`` object
        ``A``. If the second argument is set to ``true``, the
        geometric standard deviation is calculated (the default value
        for the second argument is ``false``).


    .. dseriesmethod:: B = subsample (A, d1, d2)

        |br| Returns a subsample for the period between ``d1`` and
        ``d2``. While you can achieve the same result by indexing a
        ``dseries`` object with a ``dates`` object, the ``subsample``
        method offers a more straightforward approach for programmatic
        use.

        *Example*

            ::

                >> o = dseries(transpose(1:5));
                >> o.subsample(dates('2y'),dates('4y'))

                ans is a dseries object:

                   | Variable_1
                2Y | 2
                3Y | 3
                4Y | 4


    .. dseriesmethod:: A = tag (A, a[, b, c])

        |br| Adds a tag to a variable in ``dseries`` object ``A``.

        *Example*

            ::

               >> ts = dseries(randn(10, 3));
               >> tag(ts, 'type');             % Define a tag name.
               >> tag(ts, 'type', 'Variable_1', 'Stock');
               >> tag(ts, 'type', 'Variable_2', 'Flow');
               >> tag(ts, 'type', 'Variable_3', 'Stock');


    .. dseriesmethod:: B = tex_rename (A, name, newtexname)
                       B = tex_rename (A, newtexname)
                       tex_rename_ (A, name, newtexname)
                       tex_rename_ (A, newtexname)

        |br| Updates the TeX name of the variable ``name`` to
        ``newtexname`` in the ``dseries`` object ``A``. Returns an
        updated ``dseries`` object.

        With just two arguments, ``A`` and ``newtexname``, this
        function redefines the TeX names of the entries in ``A`` to
        those specified in ``newtexname``. The ``newtexname`` argument
        must be a cell row character arrays containing the same number of
        entries as there are variables in ``A``.


    .. dseriesmethod:: B = uminus(A)

        |br| Overloads the ``uminus`` operator (``-``, unary minus)
        for the ``dseries`` object.

        *Example*

            ::

                >> ts0 = dseries(1)

                ts0 is a dseries object:

                   | Variable_1
                1Y | 1

                >> ts1 = -ts0

                ts1 is a dseries object:

                   | Variable_1
                1Y | -1


    .. dseriesmethod:: D = vertcat (A, B[, ...])

        |br| Overloads the ``vertcat`` method in MATLAB/Octave for
        ``dseries`` objects. This method facilitates the appending of
        additional observations to a ``dseries`` object. It returns a
        new ``dseries`` object, ``D``, which contains the variables
        from the input ``dseries`` objects. All input arguments must
        be ``dseries`` objects that share the same variables but are
        defined over different time ranges.

        *Example*

            ::

                >> ts0 = dseries(rand(2,2),'1950Q1',{'nifnif';'noufnouf'});
                >> ts1 = dseries(rand(2,2),'1950Q3',{'nifnif';'noufnouf'});
                >> ts2 = [ts0; ts1]

                ts2 is a dseries object:

                       | nifnif   | noufnouf
                1950Q1 | 0.82558  | 0.31852
                1950Q2 | 0.78996  | 0.53406
                1950Q3 | 0.089951 | 0.13629
                1950Q4 | 0.11171  | 0.67865


    .. dseriesmethod:: B = vobs (A)

        |br| Returns the count of variables in the ``dseries`` object ``A``.

        *Example*

            ::

                >> ts0 = dseries(randn(10,2));
                >> ts0.vobs

                ans =

                    2


    .. dseriesmethod:: B = ydiff (A)
                       B = ygrowth (A)
                       ydiff_ (A)
                       ygrowth_ (A)

        |br| Calculates annual differences or growth rates.


.. _x13-members:

X-13 ARIMA-SEATS interface
==========================

.. class:: x13

    |br| The x13 class provides a method for each X-13 command as
    documented in the X-13 ARIMA-SEATS reference manual (`x11`,
    `automdl`, `estimate`, ...). The respective options (see Chapter 7 of U.S. Census Bureau (2020))
    can then be passed by key/value pairs. The ``x13`` class has 22 members:

    :arg y: ``dseries`` object with a single variable.
    :arg x: ``dseries`` object with an arbitrary number of variables (to be used in the REGRESSION block).
    :arg arima: structure containing the options of the ARIMA model command.
    :arg automdl: structure containing the options of the ARIMA model selection command.
    :arg regression: structure containing the options of the Regression command.
    :arg estimate: structure containing the options of the estimation command.
    :arg transform: structure containing the options of the transform command.
    :arg outlier: structure containing the options of the outlier command.
    :arg forecast: structure containing the options of the forecast command.
    :arg check: structure containing the options of the check command.
    :arg x11: structure containing the options of the X11 command.
    :arg force: structure containing the options of the force command.
    :arg history: structure containing the options of the history command.
    :arg metadata: structure containing the options of the metadata command.
    :arg identify: structure containing the options of the identify command.
    :arg pickmdl: structure containing the options of the pickmdl command.
    :arg seats: structure containing the options of the seats command.
    :arg slidingspans: structure containing the options of the slidingspans command.
    :arg spectrum: structure containing the options of the spectrum command.
    :arg x11regression: structure containing the options of the x11Regression command.
    :arg results: structure containing the results returned by x13.
    :arg commands: cell array containing the list of commands.

    All these members are private. The following constructors are available:

    .. construct:: x13 (y)

        |br| Instantiates an ``x13`` object with `dseries` object
        ``y``. The ``dseries`` object passed as an argument must
        contain only one variable, the one we need to pass to X-13.


    .. construct:: x13 (y, x)

        |br| Instantiates an ``x13`` object with `dseries` objects
        ``y`` and ``x``. The first ``dseries`` object passed as an
        argument must contain only one variable, the second
        ``dseries`` object contains the exogenous variables used by
        some of the X-13 commands. Both objects must be defined on the
        same time span.


    The following methods allow to set sequence of X-13 commands, write an `.spc` file, and run the X-13 binary:


    .. x13method:: A = arima (A, key, value[, key, value[, [...]]])

        Interface to the ``arima`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = automdl (A, key, value[, key, value[, [...]]])

        Interface to the ``automdl`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = regression (A, key, value[, key, value[, [...]]])

        Interface to the ``regression`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = estimate (A, key, value[, key, value[, [...]]])

        Interface to the ``estimate`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = transform (A, key, value[, key, value[, [...]]])

        Interface to the ``transform`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs. For example, the key/value pair ``function,log``
        instructs the use of a multiplicative instead of an additive seasonal pattern,
        while ``function,auto`` triggers an automatic selection between the two based
        on their fit.


    .. x13method:: A = outlier (A, key, value[, key, value[, [...]]])

        Interface to the ``outlier`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = forecast (A, key, value[, key, value[, [...]]])

        Interface to the ``forecast`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = check (A, key, value[, key, value[, [...]]])

        Interface to the ``check`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = x11 (A, key, value[, key, value[, [...]]])

        Interface to the ``x11`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = force (A, key, value[, key, value[, [...]]])

        Interface to the ``force`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = history (A, key, value[, key, value[, [...]]])

        Interface to the ``history`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = metadata (A, key, value[, key, value[, [...]]])

        Interface to the ``metadata`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = identify (A, key, value[, key, value[, [...]]])

        Interface to the ``identify`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = pickmdl (A, key, value[, key, value[, [...]]])

        Interface to the ``pickmdl`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = seats (A, key, value[, key, value[, [...]]])

        Interface to the ``seats`` command, see the X-13 ARIMA-SEATS
        reference manual. All the options must be passed by key/value
        pairs.


    .. x13method:: A = slidingspans (A, key, value[, key, value[, [...]]])

        Interface to the ``slidingspans`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = spectrum (A, key, value[, key, value[, [...]]])

        Interface to the ``spectrum`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: A = x11regression (A, key, value[, key, value[, [...]]])

        Interface to the ``x11regression`` command, see the X-13
        ARIMA-SEATS reference manual. All the options must be passed
        by key/value pairs.


    .. x13method:: print (A[, basefilename])

        Prints an ``.spc`` file with all the X-13 commands. The
        optional second argument is a row char array specifying the
        name (without extension) of the file.


    .. x13method:: run (A)

        Calls the X-13 binary and run the previously defined
        commands. All the results are stored in the structure
        ``A.results``. When it makes sense these results are saved in
        ``dseries`` objects (*e.g.* for forecasts or filtered variables).

    .. x13method:: clean (A)

        Removes the temporary files created by an x13 run that store the intermediate
        results. This method allows keeping the main folder clean but will also
        delete potentially important debugging information.

    *Example*

            ::

                >> ts = dseries(rand(100,1),'1999M1');
                >> o = x13(ts);

                >> o.x11('save','(d11)');
                >> o.automdl('savelog','amd','mixed','no');
                >> o.outlier('types','all','save','(fts)');
                >> o.check('maxlag',24,'save','(acf pcf)');
                >> o.estimate('save','(mdl est)');
                >> o.forecast('maxlead',18,'probability',0.95,'save','(fct fvr)');

                >> o.run();

        The above example shows a run of X13 with various commands an options specified.


    *Example*

            ::

                %   1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960
                y = [112  115  145  171  196  204  242  284  315  340  360  417 ...   % Jan
                     118  126  150  180  196  188  233  277  301  318  342  391 ...   % Feb
                     132  141  178  193  236  235  267  317  356  362  406  419 ...   % Mar
                     129  135  163  181  235  227  269  313  348  348  396  461 ...   % Apr
                     121  125  172  183  229  234  270  318  355  363  420  472 ...   % May
                     135  149  178  218  243  264  315  374  422  435  472  535 ...   % Jun
                     148  170  199  230  264  302  364  413  465  491  548  622 ...   % Jul
                     148  170  199  242  272  293  347  405  467  505  559  606 ...   % Aug
                     136  158  184  209  237  259  312  355  404  404  463  508 ...   % Sep
                     119  133  162  191  211  229  274  306  347  359  407  461 ...   % Oct
                     104  114  146  172  180  203  237  271  305  310  362  390 ...   % Nov
                     118  140  166  194  201  229  278  306  336  337  405  432 ]'; % Dec

                ts = dseries(y,'1949M1');
                o = x13(ts);
                o.transform('function','auto','savelog','atr');
                o.automdl('savelog','all');
                o.x11('save','(d11 d10)');
                o.run();
                o.clean();

                y_SA=o.results.d11;
                y_seasonal_pattern=o.results.d10;

                figure('Name','Comparison raw data and SAed data');
                plot(ts.dates,log(o.y.data),ts.dates,log(y_SA.data),ts.dates,log(y_seasonal_pattern.data))


        The above example shows how to remove a seasonal pattern from a time series.
        ``o.transform('function','auto','savelog','atr')`` instructs the subsequent
        ``o.automdl()`` command to check whether an additional or a multiplicative
        pattern fits the data better and to save the result. The result is saved in
        `o.results.autotransform`, which in the present example indicates that a
        log transformation, i.e. a multiplicative model was preferred. The ``o.automdl('savelog','all')`` automatically selects a fitting
        ARIMA model and saves all relevant output to the .log-file. The ``o.x11('save','(d11, d10)')`` instructs
        ``x11`` to save both the final seasonally adjusted series ``d11`` and the final seasonal factor ``d10``
        into ``dseries`` with the respective names in the output structure ``o.results``.  ``o.clean()`` removes the
        temporary files created by ``o.run()``. Among these are the ``.log``-file storing
        summary information, the ``.err``-file storing information on problems encountered,
        the ``.out``-file storing the raw output, and the `.spc`-file storing the specification for the `x11` run.
        There may be further files depending on the output requested. The last part of the example reads out the
        results and plots a comparison of the logged raw data and its log-additive decomposition into a
        seasonal pattern and the seasonally adjusted series.

Miscellaneous
=============

Time aggregation
----------------

    |br| A set of functions allows to convert time series to lower frequencies:

          - ``dseries2M`` converts daily time series object to monthly
            time series object.

          - ``dseries2Q`` converts daily or monthly time series object
            to quarterly time series object.

          - ``dseries2S`` converts daily, monthly, or quarterly time
            series object to bi-annual time series object.

          - ``dseries2Y`` converts daily, monthly, quarterly, or
            bi-annual time series object to annual time series object.


    |br| All these routines have two mandatory input arguments: the first one is a
    ``dseries`` object, the second one the name (row char array) of the
    aggregation method. Possible values for the second argument are:

          - ``arithmetic-average`` (for growth rates),

          - ``geometric-average`` (for growth factors),

          - ``sum`` (for flow variables), and

          - ``end-of-period`` (for stock variables).

    *Example*

            ::

                >> ts = dseries(rand(12,1),'2000M1')

                ts is a dseries object:

                        | Variable_1
                2000M1  | 0.55293
                2000M2  | 0.14228
                2000M3  | 0.38036
                2000M4  | 0.39657
                2000M5  | 0.57674
                2000M6  | 0.019402
                2000M7  | 0.57758
                2000M8  | 0.9322
                2000M9  | 0.10687
                2000M10 | 0.73215
                2000M11 | 0.97052
                2000M12 | 0.60889

                >> ds = dseries2Y(ts, 'end-of-period')

                ds is a dseries object:

                      | Variable_1
                2000Y | 0.60889

Create time series with a univariate model
------------------------------------------

    |br| It is possible to expand a ``dseries`` object recursively
    with the ``from`` command. For instance to create a ``dseries`` object
    containing the simulation of an ARMA(1,1) model:

        ::

           >> e = dseries(randn(100, 1), '2000Q1', 'e', '\varepsilon');
           >> y = dseries(zeros(100, 1), '2000Q1', 'y');
           >> from 2000Q2 to 2024Q4 do y(t)=.9*y(t-1)+e(t)-.4*e(t-1);
           >> y

           y is a dseries object:

                  | y
           2000Q1 | 0
           2000Q2 | -0.95221
           2000Q3 | -0.6294
           2000Q4 | -1.8935
           2001Q1 | -1.1536
           2001Q2 | -1.5905
           2001Q3 | 0.97056
           2001Q4 | 1.1409
           2002Q1 | -1.9255
           2002Q2 | -0.29287
                  |
           2022Q2 | -1.4683
           2022Q3 | -1.3758
           2022Q4 | -1.2218
           2023Q1 | -0.98145
           2023Q2 | -0.96542
           2023Q3 | -0.23203
           2023Q4 | -0.34404
           2024Q1 | 1.4606
           2024Q2 | 0.901
           2024Q3 | 2.4906
           2024Q4 | 0.79661



    The expression following the ``do`` keyword can be any univariate
    equation, the only constraint is that the model cannot have
    leads. It can be a static equation, or a very nonlinear backward
    equation with an arbitrary number of lags. The ``from`` command
    must be followed by a range, which is separated from the
    (recursive) expression to be evaluated by the ``do`` command.
