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, we saw how the SARIMAX model can be used to include the impact of exogenous variables on our target time series. With the SARIMAX model, the relationship is unidirectional, we assume that the exogenous variable has an impact on 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 case, it would be useful to have a model than can take this bidirectional relationship into account and output predictions for both time series simultaneously.
This brings us to the vector autoregression model or VAR. This particular model allows to capture the relationship between multiple time series as they change over time. This in turn allows us to produce forecasts for many time series simultaneously, therefore performing multivariate forecasting.
Throughout this chapter, we will use the same dataset as in chapter 9. This time, we will explore the relationship between real disposable income and real consumption as shown in figure 10.1.