Hey, I would like to write a code involving automatic selection of a best composite model using ETS as well as autoregressive models. What is the criteria I should base my selection on?
Also if I'm using the auto.arima function for deducing number of AR terms and corresponding coefficients from the forecast package in R, does my input series necessarily have to be stationary? or the value for d would be automatically selected thus returning a non-stationary model?
Thanks, Phani
I will try answering the second part of your question. Your series do not need to be mean stationary, auto.arima would find an appropriate number of difference if it decides that the series has non-stationary mean. However, your series have to be variance stationary, auto.arima does not do power transformations to "stationarize" the variance of a series.
It would help if you read the help pages. The help provided for ets() and auto.arima() is quite detailed and contains the information you ask for.
Use whichever criterion you prefer. The default criterion for ets() is AIC. This is asymptotically equivalent to leave-one-out cross-validation, and so is a good choice for forecasting. The AICc is a small-sample correction of the AIC and so is arguably slightly better.
auto.arima() selects the d value using unit-root tests. So your data do not have to be stationary in the mean. However, as noted by Samik R., there is no attempt to find a transformation to stabilize the variance.