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Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

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  • K. D. Patterson
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    Abstract

    Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760600994638
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 34 (2007)
    Issue (Month): 1 ()
    Pages: 23-45

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    Handle: RePEc:taf:japsta:v:34:y:2007:i:1:p:23-45

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    Related research

    Keywords: Autoregressive model; bias; first-order correction; bootstrap bias correction; recursive mean adjustment;

    References

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    1. Mackinnon, J.G. & Smith, A.A., 1996. "Approximate Bias Correction in Econometrics," G.R.E.Q.A.M. 96a14, Universite Aix-Marseille III.
    2. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    3. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
    4. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    5. Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
    6. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages S2-S18, 09.
    7. Shin, Dong Wan & So, Beong Soo, 2000. "Gaussian tests for seasonal unit roots based on Cauchy estimation and recursive mean adjustments," Journal of Econometrics, Elsevier, vol. 99(1), pages 107-137, November.
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    Cited by:
    1. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    2. repec:rdg:wpaper:em-dp2013-02 is not listed on IDEAS
    3. Tom Engsted & Thomas Q. Pedersen, 2011. "Bias-correction in vector autoregressive models: A simulation study," CREATES Research Papers 2011-18, School of Economics and Management, University of Aarhus.
    4. Saeed Heravi & Kerry Patterson, 2013. "Log-Periodogram Estimation of the Long-Memory Parameter: An Evaluation of Competing Estimators," Economics & Management Discussion Papers em-dp2013-02, Henley Business School, Reading University.

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