FANPAC MT

FANPAC MT 3.0

This is an Application Module for estimating parameters of univariate and multivariate Generalized Autoregressive Conditionally Heteroskedastic (GARCH) models.

Features

  • Univariate ARCH, GARCH, ARMAGARCH,FIGARCH
  • Multivariate BEKK, DVEC,CCC,DCC,GO,FM,VAR
  • Normal, t, skew generalized t, multivariate skew distributions
  • Keyword interface

GARCH model with Student’s t distribution

Example

Estimate Parameters of a TGARCH model

Let

Define   where

Let

Financial time series is well-known to be fat-tailed.  For this reason we shall use the Student’s t distribution.

The log-likelihood is

where .

Specific Example

The command file for a typical problem using keyword commands looks like this:

/*  This example studies 20 years
** of monthly weighted returns **
of the Wilshire 5000 index. */
library fanpacmt;

session example 'wilshire example';
setVarNames date cwprice cwdiv cwret ewprice ewdiv ewret;
setDataSet wilshire.asc;
setSeries cwret;

estimate run1 tgarch(3,2);
showResults;

And this is the output:

==============================================================

Session: example

--------------------------------------------------------------

wilshire example

--------------------------------------------------------------

FANPAC Version 3.0.2   Data Set: wilshire  4/06/2012 12:32:42

==============================================================

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Run: run1

--------------------------------------------------------------

--------------------------------------------------------------

return code =    0

normal convergence

Model:  TGARCH

Number of Observations     : 324

Observations in likelihood : 321

Degrees of Freedom         : 313

log-likelihood :        -987.278

AIC :         1990.56

BIC :         2020.73

LRS :         1974.56

roots

_______________

1.0666476

-0.20529984 +        1.0521398i

-0.20529984 -        1.0521398i

Abs(roots)

_______________

1.0666476

1.0719824

1.0719824

Maximum likelihood covariance matrix of parameters

0.95 confidence limits computed from standard errors

Series: ewret

Variance Equation

Variance Equation Constant(s)

Estimate

4.4472

standard error

1.8130

lower confidence limit

0.88008

upper confidence limit

8.0143

Garch Parameter(s)

Estimate

0.49974

-0.60891

0.81584

standard error

0.038067

0.035513

0.041073

lower confidence limit

0.42484

-0.67878

0.73502

upper confidence limit

0.57464

-0.53903

0.89665

Arch Parameter(s)

Estimate

0.080473

0.073678

standard error

0.030695

0.028714

lower confidence limit

0.020078

0.017181

upper confidence limit

0.14087

0.13018

Mean Equations

Constant(s)

Estimate

1.7884

standard error

0.2850

lower confidence limit

1.2276

upper confidence limit

2.3492

Miscellaneous Parameters

Nu

Estimate

6.1808

standard error

1.8453

lower confidence limit

2.5501

upper confidence limit

9.8115

Platform: Windows, Mac, and Linux.

Requirements: GAUSS/GAUSS Light version 10.0 or higher.