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Bias-correction in vector autoregressive models: A simulation study

  • Tom Engsted

    ()

    (Aarhus University and CREATES)

  • Thomas Q. Pedersen

    ()

    (Aarhus University and CREATES)

We analyze and compare the properties of various methods for bias-correcting parameter estimates in vector autoregressions. 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 this simple and easy-to-use analytical bias formula compares very favorably to the more standard but also more computer intensive bootstrap bias-correction method, both in terms of bias and mean squared error. Both methods yield a notable improvement over both OLS and a recently proposed WLS estimator. We also investigate the properties of an iterative scheme when applying the analytical bias formula, and we ?find that this can imply slightly better fi?nite-sample properties for very small sample sizes while for larger sample sizes there is no gain by iterating. Finally, we also pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space during the process of correcting for bias.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-18.

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Length: 33
Date of creation: 13 May 2011
Date of revision:
Handle: RePEc:aah:create:2011-18
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Geert Bekaert & Robert J. Hodrick & David Marshall, 1996. "On biases in tests of the expectations hypothesis of the term structure of interest rates," Working Paper Series, Issues in Financial Regulation WP-96-3, Federal Reserve Bank of Chicago.
  2. Engsted, Tom & Tanggaard, Carsten, 2001. "The Danish stock and bond markets: comovement, return predictability and variance decomposition," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 243-271, July.
  3. John Y. Campbell, 1990. "A Variance Decomposition for Stock Returns," NBER Working Papers 3246, National Bureau of Economic Research, Inc.
  4. Mackinnon, J.G. & Smith, A.A., 1996. "Approximate Bias Correction in Econometrics," G.R.E.Q.A.M. 96a14, Universite Aix-Marseille III.
  5. Mark, Nelson C, 1995. "Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability," American Economic Review, American Economic Association, vol. 85(1), pages 201-18, March.
  6. Amihud, Yakov & Hurvich, Clifford M., 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(04), pages 813-841, December.
  7. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  8. 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.
  9. 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.
  10. 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.
  11. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
  12. Patterson, K. D., 2000. "Bias reduction in autoregressive models," Economics Letters, Elsevier, vol. 68(2), pages 135-141, August.
  13. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
  14. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
  15. Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
  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. Kim, Jae H, 2001. "Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 117-28, January.
  18. Kilian, Lutz, 1999. "Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 491-510, Sept.-Oct.
  19. 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.
  20. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
  21. Yakov Amihud & Clifford M. Hurvich & Yi Wang, 2009. "Multiple-Predictor Regressions: Hypothesis Testing," Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 413-434, January.
  22. K. D. Patterson, 2007. "Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-45.
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