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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).

Thanks.

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closed as not a real question by Nick Cox, Andy W, whuber Jun 18 '13 at 12:55

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

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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 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 Jun 17 '13 at 16:33
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  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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