Create a specification structure for
an ARMA(1,1)/GJR(1,1) model with conditionally t-distributed residuals:
spec = garchset('VarianceModel','GJR',...
'R',1,'M',1,'P',1,'Q',1);
spec = garchset(spec,'Display','off','Distribution','T');Note
This example is for illustration purposes only. Such an elaborate
ARMA(1,1) model is typically not needed, and should only be used after
you have performed a sound pre-estimation analysis. |
Estimate the parameters of the mean
and conditional variance models via garchfit.
Make sure that the example returns the estimated residuals and conditional
standard deviations inferred from the optimization process, so that
they can be used as presample data:
[coeff,errors,LLF,eFit,sFit] = garchfit(spec,nasdaq);
Alternatively,
you could replace this call to garchfit with
the following successive calls to garchfit and garchinfer. This is because the estimated
residuals and conditional standard deviations are also available from
the inference function garchinfer:
[coeff,errors] = garchfit(spec,nasdaq);
[eFit,sFit] = garchinfer(coeff,nasdaq);
Either approach produces the same estimation results:
garchdisp(coeff,errors)
Mean: ARMAX(1,1,0); Variance: GJR(1,1)
Conditional Probability Distribution: T
Number of Model Parameters Estimated: 8
Standard T
Parameter Value Error Statistic
----------- ----------- ------------ -----------
C 0.00099913 0.00023366 4.2759
AR(1) -0.1074 0.11568 -0.9284
MA(1) 0.26286 0.11205 2.3459
K 1.4274e-006 3.812e-007 3.7446
GARCH(1) 0.90103 0.01111 81.0988
ARCH(1) 0.048458 0.013521 3.5839
Leverage(1) 0.085677 0.016792 5.1021
DoF 7.8264 0.92862 8.4280
Store 
