Vector Autoregressive Models for Multivariate Time Series

Abstract

The vector autoregression (VAR) model is one of the most successful, flexible , and easy to use models for the analysis of multivariate time series. It is a natural extension of the univariate autoregressive model to dynamic mul-tivariate time series. The VAR model has proven to be especially useful for describing the dynamic behavior of economic and financial time series and for forecasting. It often provides superior forecasts to those from univari-ate time series models and elaborate theory-based simultaneous equations models. Forecasts from VAR models are quite flexible because they can be made conditional on the potential future paths of specified variables in the model. In addition to data description and forecasting, the VAR model is also used for structural inference and policy analysis. In structural analysis, certain assumptions about the causal structure of the data under investigation are imposed, and the resulting causal impacts of unexpected shocks or innovations to specified variables on the variables in the model are summarized. These causal impacts are usually summarized with impulse response functions and forecast error variance decompositions. This chapter focuses on the analysis of covariance stationary multivari-ate time series using VAR models. The following chapter describes the analysis of nonstationary multivariate time series using VAR models that incorporate cointegration relationships. E. Zivot et al., Modeling Financial Time Series with S-Plus®