topic Re: heteroscedasticity in daily time series in SAS Forecasting and Econometrics

heteroscedasticity in daily time series

agm65 — Thu, 15 May 2025 23:50:47 GMT

I have a electricity consumption daily time series. Data are from the last 3 years.

I have adjusted a (0,1,1) model after difference (1) the log transformed series. (checked stationarity). I have identified some outliers but any of them resulted significant when I included it as regressors.

It seems that there is not autocorrelation in the residuals (tests OK) but the heteroscedasticity tests are not fulfilled. Tried to model the residuals with arch models but cannot fix the problem of heteroscedasticity (conditional and unconditional).

Any alternatives?

proc arima data=work.series;

identify var=lvalor(1) stationarity=(dickey) nlag=30;

estimate p=(1) q=(1) noint method=ml;

*outlier maxnum=5 alpha=0.01 id=fecha;

forecast id=fecha interval=day out=b;

run;

quit;

proc model data=b;
parms const;
residual = const ;
fit residual / white breusch=(1 time);
run;
quit;

proc autoreg data=b;

model residual= / garch=(Q=2, p=2) maxit=50;

output out=out R=pepe;

run;

Re: heteroscedasticity in daily time series

sbxkoenk — Tue, 20 May 2025 09:11:43 GMT

You can read this as a starter :

Solved: Detecting Volatility in ARIMA model residuals - SAS Support Communities

Ciao,

Koen

Re: heteroscedasticity in daily time series

SASCom1 — Tue, 27 May 2025 23:54:31 GMT

In PROC AUTOREG, in addition to ARCH/GARCH model specification, you can also use HETERO statement to specify error variance function:

https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/etsug/etsug_autoreg_syntax11.htm

And the HETERO statement can also be used with GARCH model together to specify additional variables in the variance function to the standard GARCH equation as discussed here:

https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/etsug/etsug_autoreg_details12.htm#etsug.autoreg.heterogarch

PROC MODEL allows more flexible specification of error variance structures as discussed here:

https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/etsug/etsug_model_sect133.htm

If you have specific form of heteroscedasticity but not sure how to specify your model, please provide more details.