I am minimising SSE to estimate the parameters and starting values for a Holt-Winters model. I.e. "forecasting" the values using different parameters, measuring the sum of squared errors of these "forecasts" against actual historical values, and alternating the parameters to see which ones minimise SSE.
Is it possible to use "prediction" values from more than one seasonal cycle for this purpose? Presumably, once I start "forecasting" more than one cycle ahead from the start date of the retrospective "forecasts", the seasonal component will be referring to values which are influenced by the forecasts themselves. I would assume that this would make this invalid, but wondered if this was the case.
Would there be any advantage to doing this, if it were "allowed"? For example, if the slope or trend is one which has oscillated upwards and downwards over a longer time period than one cycle, would there be an advantage to incorporating more historical values?