Instead of working with just one time series, we could work with multiple series, exploiting the interrelationships between them. The true multivariate extension of ARIMA models are VARMA models, but they are rarely used in practice because they are very hard to fit. VAR models still offer us the possibility of modelling multiple time series, requiring rather loose assumptions, and a much simpler computational framework. This is an extension of the autoregressive (AR) models, where we model a time series in terms of its past.
These models arise when modeling related time series, where the past of a variable explains not only part of its own present, but also those of the rest of the variables. We will need essentially the same assumption that we required in terms of stationarity for ARIMA. Here, we will extend that to the multivariate case, and...