FANPAC MT 3.0 Example
GARCH model with Student’s t distribution
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
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: