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Bias-Correction in Vector Autoregressive Models: A Simulation Study

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  • Tom Engsted

    ()
    (CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, DK-8210 Aarhus V, Denmark)

  • Thomas Q. Pedersen

    ()
    (CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, DK-8210 Aarhus V, Denmark)

Abstract

We analyze the properties of various methods for bias-correcting parameter estimates in both stationary and non-stationary vector autoregressive models. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study, we show that when the model is stationary this simple bias formula compares very favorably to bootstrap bias-correction, both in terms of bias and mean squared error. In non-stationary models, the analytical bias formula performs noticeably worse than bootstrapping. Both methods yield a notable improvement over ordinary least squares. We pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space when correcting for bias. Finally, we consider a recently proposed reduced-bias weighted least squares estimator, and we find that it compares very favorably in non-stationary models.

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Bibliographic Info

Article provided by MDPI, Open Access Journal in its journal Econometrics.

Volume (Year): 2 (2014)
Issue (Month): 1 (March)
Pages: 45-71

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Handle: RePEc:gam:jecnmx:v:2:y:2014:i:1:p:45-71:d:34027

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Related research

Keywords: bias reduction; VAR model; analytical bias formula; bootstrap; iteration; Yule-Walker; non-stationary system; skewed and fat-tailed data;

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  1. Patterson, K. D., 2000. "Bias reduction in autoregressive models," Economics Letters, Elsevier, vol. 68(2), pages 135-141, August.
  2. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
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  4. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
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  8. James G. MacKinnon & Anthony A. Smith, Jr., . "Approximate Bias Correction in Econometrics," GSIA Working Papers 1997-36, Carnegie Mellon University, Tepper School of Business.
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  12. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
  13. Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
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  16. Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
  17. Tom Engsted & Thomas Q. Pedersen, 2008. "Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model," CREATES Research Papers 2008-27, School of Economics and Management, University of Aarhus.
  18. Michael D. Bauer & Glenn D. Rudebusch & Jing Cynthia Wu, 2012. "Correcting Estimation Bias in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 454-467, April.
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Cited by:
  1. Engsted, Tom & Pedersen, Thomas Q., 2012. "Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 241-253.
  2. Hendrik Kaufmannz & Robinson Kruse, 2013. "Bias-corrected estimation in potentially mildly explosive autoregressive models," CREATES Research Papers 2013-10, School of Economics and Management, University of Aarhus.
  3. Cavaliere, Giuseppe & Taylor, A. M. Robert & Trenkler, Carsten, 2013. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Working Papers 32993, University of Mannheim, Department of Economics.

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