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VAR Modeling and Business Cycle Analysis: A Taxonomy of Errors

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  • D.S. Poskitt

    ()

  • Wenying Yao

    ()

Abstract

In this article we investigate the theoretical behaviour of finite lag VAR(n) models fitted to time series that in truth come from an infinite order VAR(?) data generating mechanism. We show that overall error can be broken down into two basic components, an estimation error that stems from the difference between the parameter estimates and their population ensemble VAR(n) counterparts, and an approximation error that stems from the difference between the VAR(n) and the true VAR(?). The two sources of error are shown to be present in other performance indicators previously employed in the literature to characterize, so called, truncation effects. Our theoretical analysis indicates that the magnitude of the estimation error exceeds that of the approximation error, but experimental results based upon a prototypical real business cycle model indicate that in practice the approximation error approaches its asymptotic position far more slowly than does the estimation error, their relative orders of magnitude notwithstanding. The experimental results suggest that with sample sizes and lag lengths like those commonly employed in practice VAR(n) models are likely to exhibit serious errors of both types when attempting to replicate the dynamics of the true underlying process and that inferences based on VAR(n) models can be very untrustworthy.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 11/12.

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Length: 22 pages
Date of creation: 19 Apr 2012
Date of revision:
Handle: RePEc:msh:ebswps:2012-11

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Keywords: VAR; estimation error; approximation error; RBC model;

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  1. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2006. "Assessing structural VARs," International Finance Discussion Papers 866, Board of Governors of the Federal Reserve System (U.S.).
    • Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2007. "Assessing Structural VARs," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 1-106 National Bureau of Economic Research, Inc.
  2. Alasdair Scott & George Kapetanios & Adrian Pagan, 2005. "Making a match: combining theory and evidence in policy-oriented macroeconomic modelling," Computing in Economics and Finance 2005 462, Society for Computational Economics.
  3. Lippi, Marco & Reichlin, Lucrezia, 1994. "VAR analysis, nonfundamental representations, blaschke matrices," Journal of Econometrics, Elsevier, vol. 63(1), pages 307-325, July.
  4. Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
  5. Kascha, Christian & Mertens, Karel, 2009. "Business cycle analysis and VARMA models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 267-282, February.
  6. Mittnik, Stefan, 1987. "Non-recursive methods for computing the coefficients of the autoregressive and the moving-average representation of mixed ARMA processes," Economics Letters, Elsevier, vol. 23(3), pages 279-284.
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