St. errs. changed when re-running MAXIMIZE after convergence

[marinbozic]

Hi Tom,

I have noticed that repeated execution of MAXIMIZE command using last obtained parameter estimates as initial values in subsequent executions of that command yields unreasonably low standard errors of GARCH parameters.

I am running Koutmos (1996) code you posted here: http://www.estima.com/forum/viewtopic.p ... tmos#p1587

The only change I have made to the code is to duplicate the last line so to re-run MAXIMIZE after the code has reached convergence. This of course has no practical purpose in this context, other than enabling me to ask my question in a clean setting. So, the only deviation from the code you posted is that it ends with

Code: Select all

nonlin b a d g rr
maximize(pmethod=simplex,piters=2,method=bfgs,trace,iters=200) Lt start+1 end
maximize(pmethod=simplex,piters=2,method=bfgs,trace,iters=200) Lt start+1 end

Output is attached, with intermediate steps for the first MAXIMIZE run omitted for clarity.

Notice how standard errors decrease substantially from one run to the next, although likelihood did not change.

Can you please explain this effect? What should be done?

I am worried that re-starting MAXIMIZE in case of no convergence in the first run would produce incorrect standard errors.

Thanks,
Marin

[TomDoan]

This is discussed on page UG-115 in the User's Guide (v8):

Because the estimate of G produced by BFGS is used in estimating the covariance
matrix and standard errors of coefficients, you need to be careful not to apply BFGS to
a model which has already been estimated to a fairly high level of precision. If BFGS
uses fewer iterations than the number of parameters being estimated, the G will be
poorly estimated and, hence, the standard errors derived from them will be incorrect.

If you continue to read that, you'll see that the recommendation is to use the option HESSIAN=%XX on the second estimation.

[marinbozic]

Thanks, Tom!