I have two sets of time series data for 36 months. It contains seasonal trends with a 12-month cycle.

  1. How to determine whether it is a good model? The smaller the AIC, the better the model?
  2. Do I need to do any transformation before using auto.arima? As I find in google that auto.arima has already dealt with seasonal trends.
  3. Do I need to re-model if the residuals of the forecast not following $\mathcal N(0,1)$?
  4. Do I need more data to do the forecasting? (now only 3 sets of data to do forecasting, due to seasonal trends).


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    $\begingroup$ Welcome to the site, @stephen. Note that we are not here to do your analyses for you. In particular, 'plez send me the codez' questions elicit a good bit of annoyance. See if you can edit your Q to clarify substantive questions you have that don't amount to asking for someone to analyze your data for you. It may help you to read through our help page, which contains guidelines for questions. Otherwise, this question may end up being closed. $\endgroup$ – gung - Reinstate Monica Jun 17 '13 at 16:05
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    $\begingroup$ Also please bear in mind that without any context the families of model worth considering can't be determined. 'Data' doesn't mean a bare list of numbers. $\endgroup$ – Scortchi - Reinstate Monica Jun 17 '13 at 16:33
  1. AIC is often a good indicator of model quality. Lower AIC = better model. Nevertheless, don't blindly trust AIC or any other statistical measure. The only true measure of a forecasting model's quality is out of sample forecasting accuracy.

  2. Yes, auto.arima() already includes season. Be sure to tell auto.arima() that these are monthly data, i.e., don't simply plug in a vector of length 36, but a ts object.

  3. Depending on your data, you may want to look at log or other transforms if residuals are "really not normal".

  4. Three years of data should be (barely) enough for an ARIMA model. You can also look at exponential smoothing/state space models using ets().

Here is a book recommendation on forecasting.

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