topic Re: R2 calculation in autoregressive models in SAS Forecasting and Econometrics

R2 calculation in autoregressive models

olga19 — Tue, 14 Nov 2023 21:21:04 GMT

Good evening,

this is my question: is it statistically correct to calculate the R2 with the formula (Pearson correlation )^2 in an autoregressive model without intercept?

I have calculated it with the formula (Pearson correlation )^2 in a proc autoreg function calculating a backstep multivariate analysis with the method=ITYW.

Thank you in advance,

Olga

Re: R2 calculation in autoregressive models

sbxkoenk — Tue, 14 Nov 2023 21:27:51 GMT

Hello,

For autoregression, BIC | AIC and AICC are much better goodness-of-fit measures than R².

I wouldn't use R² when dealing with time series regression.

Also, you calculate the Pearson correlation between what and what?

BR, Koen

Re: R2 calculation in autoregressive models

sbxkoenk — Tue, 14 Nov 2023 21:29:22 GMT

I have moved this topic-thread to

"SAS Forecasting and Econometrics" - board.

Koen

Re: R2 calculation in autoregressive models

olga19 — Tue, 14 Nov 2023 22:48:54 GMT

Hi Koen,

I am forecasting a model using macroeconomic variables that I have
previously selected. The target variable is a default rate information and
the variables in the model are the macroeconomic variables.

I would like to know: is there a statistical reason that imposes a specific
formula for the calculation of R2 in this kind of model? Can I use this
formula or the methodology is wrong due to specific statistical assumptions?

Thanks
Olga

Re: R2 calculation in autoregressive models

Ksharp — Wed, 15 Nov 2023 03:11:10 GMT

The general formula of R2 is 1 - uss(residual)/css(Y) .

But if there is only one independent variable(a.k.a x variable), I think R2 =(Pearson correlation )^2

proc reg data=sashelp.class plot=none;
model weight=age height;
output out=want p=p r=r;
quit;

proc sql;
select 1-uss(r)/css(weight) as R_square from want;
quit;