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Chapter 4: VAR Models

Chapter 4: VAR ModelsThis Chapter describes a set of techniques which stand apart from those considered in thenext three chapters, in the sense that economic theory is only minimally used in the infer-ential process. VAR Models , pioneered by Chris Sims about 25 years ago, have acquireda permanent place in the toolkit of applied macroeconomists both to summarize the infor-mationcontainedinthedataandtocondu ctcertaintypesofpolicyexperiments. VARarewell suited for thefirst purpose: the Wold theorem insures that any vector of time serieshas a VAR representation under mild regularity conditions and this makes them the naturalstarting point for empirical analyses. We discuss the Wold theorem, and the issues con-nected with non-uniqueness, non-fundamentalness and non-orthogonality of the innovationvector in thefirst section.

example, if stationarity is not assumed there will still be a linearly regular and a linearly deterministic component even though each will have time varying coe fficients (see (4.3)). Third, if we insist on requiring covariance stationary, preliminary transformations of y† t may be needed to produce the representation (4.4).

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