topic Re: ARCH model with YW method - no rho output in SAS Forecasting and Econometrics

ARCH model with YW method - no rho output

j_elisio — Thu, 07 Dec 2023 23:04:34 GMT

Good evening,

I'm estimating a model with an autoregressive error by the Yule-Walker method using the AUTOREG procedure. In the final output (2nd regression step), SAS does not present the final parameters (rho) for each of the autoregressive terms (in my case, ar1, ar2, ar12) and corresponding standard errors. Why is SAS not showing this information in the final output?

Thank you in advance.

Re: ARCH model with YW method - no rho output

sbxkoenk — Mon, 11 Dec 2023 22:37:41 GMT

Hello,

Are you having

ODS SELECT NONE; or
ODS EXCLUDE ALL;

statement (in front of PROC AUTOREG)?

The parameter estimates are in an output object with one of these names:

ARParameterEstimates
ParameterEstimates
ParameterEstimatesGivenAR
ParameterEstimatesSCBP

You can use

ODS TRACE ON;

statement before your PROC AUTOREG to see the name of the output objects in the LOG.

Can you post your code to help us help you?

Koen

Re: ARCH model with YW method - no rho output

SASCom1 — Tue, 12 Dec 2023 17:19:39 GMT

Hello @j_elisio ,

For Yule Walker estimation, the AR parameters are estimated from sample autocorrelation functions of first step OLS residuals using Yule Walker equations. They are not estimated in the final step using GLS. The GLS step only obtain regression estimates 'beta'. So the AR parameters are only printed out in the first step of OLS results, but not in the final step parameter estimates table. The following Details section discusses Yule Walker estimation method:

https://go.documentation.sas.com/doc/en/pgmsascdc/v_045/etsug/etsug_autoreg_details02.htm#etsug_autoreg003664

The following section, specifically in item #9, discusses output layout for different estimation methods , including METHOD = YW,

https://go.documentation.sas.com/doc/en/pgmsascdc/v_045/etsug/etsug_autoreg_details57.htm

9. If the NLAG= option is specified with METHOD=ULS or METHOD=ML, the regression parameter estimates are printed again, assuming that the autoregressive parameter estimates are known. In this case, the Standard Error and related statistics for the regression estimates will, in general, be different from the case when they are estimated. Note that from a standpoint of estimation, Yule-Walker and iterated Yule-Walker methods (NLAG= with METHOD=YW, ITYW) generate only one table, assuming AR parameters are given.

I hope this helps.

Re: ARCH model with YW method - no rho output

j_elisio — Wed, 13 Dec 2023 10:25:49 GMT

Hello Koen,

Thank you for your reply.

I was expecting the initial AR estimates to change over the iteration process of the autoreg. It seems it is not the case. Nonetheless, I have the AR coefficients in the corresponding output table as you mentioned. Thank you once again.

Re: ARCH model with YW method - no rho output

j_elisio — Wed, 13 Dec 2023 10:26:32 GMT

Hello,

Thank you for your reply and clarification.

Sincerely,