Multivariate time-series models

Multivariate time-series models are designed to capture the dynamic of multiple time series simultaneously and leverage dependencies across these series for more reliable predictions. The most comprehensive introduction to this subject is Lütkepohl (2005).

Systems of equations

Univariate time-series models, like the ARMA approach we just discussed, are limited to statistical relationships between a target variable and its lagged values or lagged disturbances and exogenous series, in the case of ARMAX. In contrast, multivariate time-series models also allow for lagged values of other time series to affect the target. This effect applies to all series, resulting in complex interactions, as illustrated in the following diagram:

Figure 9.9: Interactions in univariate and multivariate time-series models

In addition to potentially better forecasting, multivariate time series are also used to gain insights into cross-series dependencies...