We want to implement simple exponential smoothing model to minimize mean square error by optimizing smoothing weights. We are using proc ESM for the same. The formula used for forecasting the values is : Ft+1 = αYt+ (1-α) Ft Ft+1= forecast for the next period α = smoothing constant Yt= observed value of series in period t (default rate) Ft= old forecast for period t We have read that in order to start the algorithm the first forecasted value is taken as first actual value i.e. : Ft =Yt where Ft is forecasted value for first iteration and Yt is the actual value. When we are running the proc esm code , the first forecasted value in output dataset is not equal to the first actual value. Please find the attached excel sheet of Time Series Data :input data and corresponding output data. Level smoothing weight(α ) is taken as :0.6833 (automatically optimized by proc esm) and mean square error comes out to be :0.00264115 Please let us know how the first predicted value is being calculated in the output table.
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