The "Forecasting Process Details" section of the Time Series Forecasting System documentation in the SAS/ETS User's Guide discusses the relationship between various exponential smoothing models and ARIMA models. PROC ARIMA fits the single exponential smoothing model with an optimal smoothing weight as shown below:

proc arima data=work.a;
   title 'Single exponential smoothing with optimal smoothing weight';
   identify var=y(1);
   estimate q=1 noconstant;
   run;

The optimal smoothing weight is equal to (1-theta), where theta is the MA(1) parameter that is estimated by the ARIMA procedure.

Double and triple exponential smoothing models have ARIMA model equivalents. However, they involve restrictions on the fitted moving average parameters. Details about the parametric restrictions needed for ARIMA model specifications of the double and triple exponential smoothing models are included in the aforementioned Time Series Forecasting System documentation.

Because PROC ARIMA does not support parametric restrictions, only approximations to the double and triple exponential smoothing models can be specified in the ARIMA procedure. The approximations to the double and triple exponential smoothing models are shown below, respectively:

proc arima data=work.a;
   title 'ARIMA approximation to Double exponential smoothing model';
   identify var=y(1,1);
   estimate q=(1)(1) noconstant;
   run;

proc arima data=work.a;
   title 'ARIMA approximation to Triple exponential smoothing model';
   identify var=y(1,1,1);
   estimate q=(1)(1)(1) noconstant;
   run;