6.
Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis 6.4.4. Univariate Time Series Models 6.4.4.6. BoxJenkins Model Identification


Example for Southern Oscillations 
We show typical series of plots for the initial model identification
stages of BoxJenkins modeling for two different examples.
The first example is for the southern oscillations data set. We start with the run sequence plot and seasonal subseries plot to determine if we need to address stationarity and seasonality. 

Run Sequence Plot 
The run sequence plot indicates stationarity. 

Seasonal Subseries Plot 
The seasonal subseries plot indicates that there is no significant seasonality. Since the above plots show that this series does not exhibit any significant nonstationarity or seasonality, we generate the autocorrelation and partial autocorrelation plots of the raw data. 

Autocorrelation Plot 
The autocorrelation plot shows a mixture of exponentially decaying and damped sinusoidal components. This indicates that an autoregressive model, with order greater than one, may be appropriate for these data. The partial autocorrelation plot should be examined to determine the order. 

Partial Autocorrelation Plot 
The partial autocorrelation plot suggests that an AR(2) model might be appropriate. In summary, our intial attempt would be to fit an AR(2) model with no seasonal terms and no differencing or trend removal. Model validation should be performed before accepting this as a final model. 