6 Modeling complex time series

 

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.

6.1 Forecasting bandwidth usage for data centers

6.2 Examining the autoregressive moving average process

6.3 Identifying a stationary ARMA process

6.4 Devising a general modeling procedure

6.4.1 Understanding the Akaike information criterion (AIC)

6.4.2 Selecting a model using the AIC

6.4.3 Understanding residual analysis

6.4.4 Performing residual analysis

6.5 Applying the general modeling procedure

6.6 Forecasting bandwidth usage

6.7 Next steps

6.8 Exercises

Summary