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8 - Vector Autoregression for Stationary Time Series

from Part III - Multiple-equation Regression Models

Published online by Cambridge University Press:  18 June 2026

Suzanna Linn
Affiliation:
Pennsylvania State University
Matthew J. Lebo
Affiliation:
University of Western Ontario
Clayton Webb
Affiliation:
University of Kansas
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Summary

In this chapter we examine multi-equation models for stationary data – vector autoregression. We describe a general system of equations in which each variable is allowed to be a function of contemporaneous values of all other variables, as well as lags of itself, and all other variables in the system. We explain the estimation problem inherent in a system with contemporaneous relationships and show how this estimation problem is solved by rewriting the system in reduced form. While this system can be estimated, writing the system in reduced form trades the estimation problem for an identification problem. We then describe how to build a reduced form VAR and discuss the interpretational tools widely used in VAR analysis. We cover some extensions of the VAR model and discuss the role of Granger causality in VAR analysis. We offer a practical guide to VAR analysis, including the basic steps in the framework, and provide an example using a five-variable system of attention allocation using Twitter data.

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