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:
http://monogan.myweb.uga.edu/teaching/ts/ (see link to "ARIMA Models")