Abstract
This chapter introduces multivariate time series analysis and, in particular, it focuses on vector autoregressive (VAR) models. Section 3.1 extends the concept of weak stationarity to a multivariate framework and shows how to compute cross-covariance and cross-correlation matrices. Section 3.2 introduces VAR models in their structural and reduced forms, and explains under which identification conditions it is possible to go from one form to the other; additionally, in this section we discuss the key properties of the model and how its structure may be specified and estimated. Finally, we show how VAR models can be used in forecasting applications. Section 3.3 discusses VAR analysis, including impulse response functions the variance decomposition, and Granger causality. Finally, Section 3.4 briefly describes the vector moving average and the VAR moving average models.
Keywords: Vector autoregressive model; Choleski decomposition; impulse response functions analysis; variance decomposition; Granger causality
Supplementary material: Online appendix
Essentials of Time Series for Financial Applications 