Information criterions in exp smoothing models

What are the numbers of parameters to be penalized for when using information criterions(BIC or AIC or..) for selecting the best models? Let's say that we have 3 models: 1. Simple exponential smoothing 2. Holt's method(level+trend) 3. Holt Winters(L+T+S), where开发者_如何学运维 we have monthly seasonality. How many parameters for penalization does have each model?

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I agree that this is not an R question, but it is, nevertheless, a valid time-series question. As far as I know, the theory is not very clear on how the IC is calculated for exponential smoothing models. But there have been few studies. See, for example, this paper. See also Prof. Hyndman's comment to a related question here.

Be careful - don't use IC to compare between, for e.g., exponential smoothing and ARIMA models. See the comment in this post.