Exponential Smoothing and the Akaike Information Criterion

Using an innovations state space approach, it has been found that the Akaike information criterion (AIC) works slightly better, on average, than prediction validation on withheld data, for choosing between the various common methods of exponential smoothing for forecasting. There is, however, a puzzle. Should the count of the seed states be incorporated into the penalty term in the AIC formula? We examine arguments for and against this practice in an attempt to find an acceptable resolution of this question.