Vector Autoregressions

Vector autoregressions (VAR’s) are dynamic models of a group of time series. In “Macroeconomics and Reality” and later papers, Sims has proposed using VAR’s as an alternative to large simultaneous equations models for studying the relationship among the important aggregates. The two main uses of this methodology are:

•to test formally theories which imply particular behavior for the vector autoregression.

•to learn more about the historical dynamics of the economy.

With the use of Bayesian techniques, VAR’s have also been employed very successfully for small multivariate forecasting models.

VAR’s have become a key tool in modern macroeconometrics. While there is some coverage of the topic in econometrics books such as Greene (2012) and introductory time series books like Diebold (2004), we would recommend more specialized books such as Enders (2014), Hamilton (1994) and Lütkepohl (2006). Of these, Enders is the most applied; the others are more theoretical.

In addition to those, the notes from our Vector Autoregression e-course can be very helpful.

The topics covered are:

Historical Decomposition

Structural VAR's

Blanchard-Quah/Long-Run Restrictions

Generalized Impulse Responses

Conditional Forecasting and Counterfactuals

Cointegration and Error Correction Models

Near-VAR's

Forecasting: a Bayesian Perspective

Kalman Filter