I'm not a statistician, so I would love an easy to understand answer. Is there a maximum likelihood estimator that can be stated as an explicit function of the observed data for the models enumerated below? If yes, what are the functions? I assume there's a different function for each parameter, right?
- Holt-Winter double exponential smoothing // for parameters a and b
- Brown's double exponential smoothing // for parameters a and b
- Peter Winters' triple exponential smoothing // for parameters a, b, and y.
I use the wikipedia definitions of these exponential smoothing models as defined in http://en.wikipedia.org/wiki/Exponential_smoothing#Double_exponential_smoothing
If the answer is that there is no explicit function for the maximum likelihood estimators for these models, is there any other type of explicit function that can be used to estimate the parameters? I'm only looking for explicit functions of the observed data, not optimization programs.
Thanks so much to anyone who can help!