ARIMA Model Fitting Guidelines

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

MODEL IDENTIFICATION

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.

Differencing

  • 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: