Covariance matrix of coefficients with GARCH models

[strypste]

HI there

I estimated a GARCH model and now I want to calculate the variance covariance matrix of the coefficients (I can obtain this by View -> Covariance matrix). HoBut how is this calculated in Eviews?

As there is a constant in the mean and variance equation, X'X is not invertible, where X is a matrix of all the regressors in the model. So how can we possible do this?

Best
S

[startz]

A thoughtful question, but why do you think X'X is not invertible? The variables in the mean and variance equations don't enter linearly.

[strypste]

Hi Startz

Thanks for your answer. So how can I calculate it then? I looked online and textbooks, but was unsuccessful in finding an answer. Any references?

Best
s

[startz]

I believe the GARCH variance is just the usual maximum likelihood variance estimator, but maybe one of the EViews folks or Trubador could chime in.

[trubador]

Startz is right. You can try the following and see it for yourself:

Code: Select all

'Create a workfile wfcreate u 1000 'Generate an exogenous series series x = nrnd 'Generate a y series that follows a GARCH-X(1,1) dynamic (use TSDGP add-in) tsdgp(meanconst="5",meanexog="2*x",varconst="1", arch = "0.08", garch="0.91") y 'Estimate the model equation eq.arch(backcast=1) y c x 'Save the gradients and store as a matrix eq.makegrads(n=grads) stom(grads,gradmat) 'Compute the covariance matrix (OPG) sym varcov=@inverse(@transpose(gradmat)*gradmat) 'Save the covariance matrix from the estimated equation for comparison sym eqcov = eq.@coefcov

[strypste]

Brilliant! Thanks you so much for this. Very much appreciated!

Best
s