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ARIMA Model Fitting Guidelines

Guidelines for fitting ARIMA models.  Includes Box-Jenkins guidance.


Check for stationarity of the time series.
  • If the mean is not stationary, then explore differencing.
    • Look at both nonseasonal and seasonal stationarity.
  • How to check?
  • Examine the acf and pacf of the original time series.
  • Augmented Dickey-Fuller test.
  • If the variance is not stationary, explore a pre-differencing transform (Bowerman chapter 11)
    • For instance, if variation increases steadily over time.
  • How to check?
  • Graphically.

  • Non-seasonal
  • Seasonal

Three-step procedure for tentatively identifying a model (Bowerman p. 533)
  • Step 1: Use the behavior of the ACF and PACF at the non-seasonal level 
  • Step 2: Use the behavior of the ACF and PACF at the seasonal level
  • Step 3: Combine the models

How many observations?
  • Recommended that 50 or preferably more observations should be initially considered. (Montgomery p. 265)
  • If the model includes seasonal components, it helps to have data that spans several seasons.

Have knowledge of the underlying process that generates the data.  (Montgomery p. 265)

Generic R code for exploring and fitting an ARIMA model is included at the bottom of this page.  See file "misc arima R code.txt".

Online references that provide helpful guidance include: