Vector Autoregression Analysis: Estimation and Interpretation

Vector Autoregression Analysis: Estimation andInterpretationJohn E. FloydUniversity of Toronto September 19, 20051 IntroductionThis expositional paper lays out the mechanics of running and interpretingvector autoregressions. It proves no theorems. Rather, it sets out the basicsof how VAR s work and outlines some fundamentals regarding interpreta-tion. For the theoretical details, see Walter Enders,Applied EconometricTime Series, John Wiley & Sons, 1995, pp. 291 353 and earlier material asrequired, Helmut L utkepohl,Introduction to Multiple Time Series Analysis,Springer-Verlag, 1991, pp. 9 27, 43 58, and 97 117, and James D. Hamil-ton,Time Series Analysis, Princeton University Press, 1994, pp. 257 372and earlier material as The Underlying Economic ModelConsider the following economic model with two variablesy1andy2, eachof which depends on itself lagged, on the current and lagged values of theother variable and on aiiderror term:y1(t)=v10+v12y2(t)+a11y1(t 1)+a12y2(t 2)+e1(t)(1)y2(t)=v20+v21y1(t)+a21y1(t 1)+a22y2(t 2)+e2(t)(2) This is written to help students understand how to run VARs.

Vector Autoregression Analysis: Estimation and Interpretation John E. Floyd University of Toronto⁄ September 19, 2005 1 Introduction This expositional paper lays out the mechanics of running and interpreting vector autoregressions. It proves no theorems. Rather, it sets out the basics

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