10 Forecasting multiple time series

 

This chapter covers

  • Examining the VAR model
  • Exploring Granger causality to validate the use of the VAR model
  • Forecasting multiple time series using the VAR model

In the last chapter, you saw how the SARIMAX model can be used to include the impact of exogenous variables on a time series. With the SARIMAX model, the relationship is unidirectional: we assume that the exogenous variable has an impact on the target only.

However, it is possible that two time series have a bidirectional relationship, meaning that time series t1 is a predictor of time series t2, and time series t2 is also a predictor for time series t1. In such a case, it would be useful to have a model that can take this bidirectional relationship into account and output predictions for bothtime series simultaneously.

This brings us to the vector autoregression (VAR) model. This particular model allows us to capture the relationship between multiple time series as they change over time. That, in turn, allows us to produce forecasts for many time series simultaneously, therefore performing multivariate forecasting.

Throughout this chapter, we will use the same US macroeconomics dataset as in chapter 9. This time we’ll explore the relationship between real disposable income and real consumption, as shown in figure 10.1.

10.1 Examining the VAR model

10.2 Designing a modeling procedure for the VAR(p) model

10.2.1 Exploring the Granger causality test

10.3 Forecasting real disposable income and real consumption

10.4 Next steps

10.5 Exercises

10.5.1 Use a VARMA model to predict realdpi and realcons

10.5.2 Use a VARMAX model to predict realdpi and realcons

Summary