This chapter covers
- Examining the autoregressive moving average model or ARMA(p,q)
- Experimenting with the limitations of the ACF and PACF plots
- Selecting the best model with the Akaike information criterion (AIC)
- Analyzing a time series model using residual analysis
- Building a general modeling procedure
- Forecasting using the ARMA(p,q) model
In chapter 4 we covered the moving average process, denoted as MA(q)), where q is the order. You learned that in a moving average process, the present value is linearly dependent on the mean, the current error term, and past error terms. The order q can be inferred using the ACF plot, where autocorrelation coefficients will be significant up until lag q only. In the case where the ACF plot shows a slowly decaying pattern or a sinusoidal pattern, it is possible that you are in the presence of an autoregressive process instead of a moving average process.