garchFit
========

Purpose
-------
Estimates univariate GARCH model.

Format
------

.. function:: out1 = garchFit(y, p [, q, c0])
              out1 = garchFit(dataset, formula, p [, q, c0])

   :param y: dependent variables.
   :type y: Matrix

   :param x: independent variables.
   :type x: Matrix

   :param dataset: name of data set or null string.
   :type dataset: string

   :param formula: formula string of the model. E.g. ``"y ~ X1 + X2"`` 'y' is the name of dependent variable, '``X1``' and '``X2``' are names of independent variables; E.g. ``"y ~ ."`` , '.' means including all variables except dependent variable 'y';
   :type formula: string

   :param p: order of the GARCH parameters.
   :type p: scalar

   :param q: Optional input. order of the ARCH parameters.
   :type q: scalar

   :param c0: Optional input. :class:`garchControl` structure.

      .. list-table::
         :widths: auto

         * - c0.density
           - scalar, density of error term:

             :0: Normal
             :1: Student's t
             :3: skew generalized t.

         * - c0.asymmetry
           - scalar, if nonzero assymetry terms are added.
         * - c0.inmean
           - scalar, GARCH-in-mean, square root of conditional variance is included in the mean equation.
         * - c0.stConstraintsType
           - scalar, type of enforcement of stationarity requirements:

             :1: roots of characteristic polynomial constrained outside unit circle
             :2: arch, GARCH parameters constrained to sum to less than one and greater than zero
             :3: none.

         * - c0.cvConstraintsType
           - scalar, type of enforcement of nonnegative conditional variances:

             :0: direct constraints
             :1: Nelson & Cao constraints

         * - c0.covType
           - scalar, type of covariance matrix of parameters:

             :1: ML
             :2: QML
             :3: none

   :type c0: Optional input

   :return out1: garchEstimation structure containing the following members:

      .. list-table::
         :widths: auto

         * - out1.aic
           - scalar, Akiake criterion.
         * - out1.bic
           - scalar, Bayesian information criterion.
         * - out1.lrs
           - scalar, likelihood ratio statistic.
         * - out1.numObs
           - scalar, number of observations.
         * - out1.df
           - scalar, degrees of freedom.
         * - out1.par
           - instance of PV structure containing parameter estimates.
         * - out1.retcode
           - scalar, return code:

             :1: normal convergence.
             :2: forced exit.
             :3: function calculation failed.
             :4: gradient calculation failed.
             :5: Hessian calculation failed.
             :6: line search failed.
             :7: error with constraints.
             :8: function complex.

         * - out1.moment
           - KxK matrix, moment matrix of parameter estimates.
         * - out1.climits
           - Kx2 matrix, confidence limits.

   :rtype out1: struct


Example
-------

::

   new;
   cls,;
   library tsmt;

   y = loadd( getGAUSSHome() $+ "pkgs/tsmt/examples/garch.dat");

   struct garchEstimation f0;
   f0 = garchFit(y, 1, 1);


Library
-------
tsmt

Source
------
tsgarch.src

.. seealso:: Functions :func:`garchMFit`, :func:`garchGJRFit`