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Posted 08-23-2022 02:20 PM
(1005 views)

Hello,

I think I'm encountering a problem similar to this post on the forum, but as there were no replies there I thought I'd make a new one. Any insight is appreciated.

I'm using PROC AUTOREG with ML estimation for AR terms, and using backstep to backwards-eliminate the AR terms from the model. I'm using an SLSTAY of 0.1, but the backwards elimination process doesn't appear to be working as intended.

The output table shows two AR terms included in the final model with p = 0.22 and *p *= 0.25, in addition to two AR terms that correctly under the cutoff. The Backwards Elimination of AR Terms table displays an eliminated term with an even lower *p *val than those that were left in the model (*p *= 0.21).

Here is the PROC AUTOREG call:

```
proc autoreg data=model_data outest=model_est all plots;
model log_dep =
_pred1AnYoY
_pred2MA12
/STATIONARITY= (PHILLIPS) DWPROB dw=4 method=ml NLAG=15 slstay=0.1 archtest backstep;
output out=model_out p=log_yhat pm=log_ytrend lcl=lcl r=residuals ucl=ucl;
run;
```

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Because you specified method = ML, but the backward elimination is done only once on the Yule Walker estimates after the OLS step, the significance level for the AR parameters in the Yule Walker stage can be different than when the AR parameters are estimated during the ML estimation. The following section of documentation discusses how the backward elimination is done:

For method = ML, the significance level of the selected AR parameters should be consistent with the SLSTAY = level in the 'Backward Elimination of Autoregressive Terms' output table, but may not the case in the Maximum Likelihood Estimates 'Parameter Estimates' output.

I hope this helps.

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Because you specified method = ML, but the backward elimination is done only once on the Yule Walker estimates after the OLS step, the significance level for the AR parameters in the Yule Walker stage can be different than when the AR parameters are estimated during the ML estimation. The following section of documentation discusses how the backward elimination is done:

For method = ML, the significance level of the selected AR parameters should be consistent with the SLSTAY = level in the 'Backward Elimination of Autoregressive Terms' output table, but may not the case in the Maximum Likelihood Estimates 'Parameter Estimates' output.

I hope this helps.

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