Just guessing here as I do not have your results to go on, but I think it would be Fit Model. Specify Streamflow as the Y. Highlight the Precipitation, Period, and Station columns and click the Macros button. Choose Full Factorial and click Run (Note: from your description I believe you do want the three-way interaction in the model).
The interaction terms in the output will indicate if the Precipitation slope is changing for the various periods or stations. Let us know if this matches your previous analysis. If not, could you provide some of the results from that previous analysis?
Dan Obermiller