igarchFit

Purpose

Estimates integrated GARCH model, i.e., a model containing a unit root.

Format

gOut = igarchFit(y, p[, q, gCtl])
gOut = igarchFit(y, x, p[, q, gCtl])
gOut = igarchFit(dataset, formula, p[, q, gCtl])
Parameters:
  • y (Matrix) – dependent variables.
  • x (Matrix) – independent variables.
  • dataset (string) – name of data set or null string.
  • formula (string) – 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’;
  • p (scalar) – order of the GARCH parameters.
  • q (scalar) – Optional input, order of the ARCH parameters.
  • gctl –

    Optional input, garchControl structure.

    gctl.density scalar, density of error term:
    0 Normal distribution. (Default)
    1 Student’s t-distribution.
    3 Skew generalized t-distribution.
    gctl.asymmetry scalar, if nonzero assymetry terms are added. (Default = 0)
    gctl.inmean scalar, GARCH-in-mean, square root of conditional variance is included in the mean equation.
    gctl.stConstraintsType scalar, type of enforcement of stationarity requirements:
    1 Roots of characteristic polynomial constrained outside unit circle. (Default)
    2 ARCH, GARCH parameters constrained to sum to less than one and greater than zero.
    3 None.
    gctl.cvConstraintsType scalar, type of enforcement of nonnegative conditional variances:
    0 Direct constraints. (Default)
    1 Nelson & Cao constraints.
    gctl.covType scalar, type of covariance matrix of parameters:
    1 Maximum Likelihood. (Default)
    2 Quasi-Maximum Likelihood. (Default)
    3 None.
    gctl.sqpsolvemtControlProc function pointer, pointer to a function that updates optimization settings by setting the sqpsolvemtControl structure members.
    gctl.cmlmtControlProc function pointer, pointer to a function that updates optimization settings by setting the cmlmtControl structure members.
    gctl.start PV structure, estimation starting values.
Returns:

gOut –

garchEstimation structure.

gout.aic scalar, Akiake criterion.
gout.bic scalar, Bayesian information criterion.
gout.lrs scalar, likelihood ratio statistic.
gout.numObs scalar, number of observations.
gout.df scalar, degrees of freedom.
gout.par instance of PV structure containing parameter estimates.
gout.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.
gout.moment KxK matrix, moment matrix of parameter estimates.
gout.climits Kx2 matrix, confidence limits.
gout.tsmtDesc

An instance of the tsmtModelDesc structure containing the following members:

tsmtDesc.depvar Kx1 string array, names of endogenous variables.
tsmtDesc.indvars Mx1 string array, names of exogenous variables.
tsmtDesc.timespan 2x1 string array, range of the time series. Available if date vector is passed as part of a dataframe input.
tsmtDesc.ncases Scalar, number of observations.
tsmtDesc.df Scalar, degrees of freedom.
tsmtDesc.model_name String, model name.
gout.sumStats

An instance of the tsmtSummaryStats structure containing the following members:

sumStats.sse Vector, sum of the squared errors of estimates for endogenous variables in the model.
sumStats.mse Vector, mean squared errors of estimates for endogenous variables in the model.
sumStats.rmse Vector, root mean squared errors of estimates for endogenous variables in the model.
sumStats.see Vector, standard error of the estimates for endogenous variables in the model.
sumStats.rsq Vector, r-squared of estimates for endogenous variables in the model.
sumStats.AdjRsq Scalar, adjusted r-squared of estimates for endogenous variables in the model.
sumStats.ssy Scalar, total sum of the squares for endogenous variables in the model.
sumStats.DW Scalar, Durbin-Watson statistic for residuals from the estimates for endogenous variables in the model.

Example

new;
cls;
library tsmt;

y = loadd(getGAUSSHome("pkgs/tsmt/examples/igarch.dat"));

struct garchEstimation gOut;
gOUt = igarchFit(y, 1, 1);

This prints the following output:

================================================================================
Model:                 I-GARCH(1,1)          Dependent variable:               Y
Time Span:                  Unknown          Valid cases:                    300
================================================================================
                             Coefficient            Upper CI            Lower CI

          beta0[1,1]             0.02710            -0.04224             0.09644
          garch[1,1]             0.81404             0.71688             0.91120
           arch[1,1]             0.18596             0.06604             0.30587
          omega[1,1]             0.01468            -0.00739             0.03675
================================================================================

                AIC:                                                  -635.63652
                LRS:                                                  -643.63652

Library

tsmt

Source

tsgarch.src