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Half-Life Estimation based on the Bias-Corrected Bootstrap: A Highest Density Region Approach

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  • Jae Kim

    ()

  • Param Silvapulle

    ()

  • Rob J. Hyndman

    ()

Abstract

The half-life is defined as the number of periods required for the impulse response to a unit shock to a time series to dissipate by half. It is widely used as a measure of persistence, especially in international economics to quantify the degree of mean reversion of the deviation from an international parity condition. Several studies have proposed bias-corrected point and interval estimation methods. However, they have found that the confidence intervals are rather uninformative with their upper bound being either extremely large or infinite. This is largely due to the distribution of the half-life estimator being heavily skewed and multi-modal. In this paper, we propose a bias-corrected bootstrap procedure for the estimation of half-life, adopting the highest density region (HDR) approach to point and interval estimation. Our Monte Carlo simulation results reveal that the bias-corrected bootstrap HDR method provides an accurate point estimator, as well as tight confidence intervals with superior coverage properties to those of its alternatives. As an application, the proposed method is employed for half-life estimation of the real exchange rates of seventeen industrialized countries. The results indicate much faster rates of mean-reversion than those reported in previous studies.

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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 11/06.

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Length: 35 pages
Date of creation: Jun 2006
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Handle: RePEc:msh:ebswps:2006-11

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Keywords: Autoregressive Model; Bias-correction; Bootstrapping; Confidence interval; Half-life; Highest density region.;

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References

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  1. Rossi, Barbara, 2002. "Confidence Intervals for Half-life Deviations from Purchasing Power Parity," Working Papers 02-08, Duke University, Department of Economics.
  2. Guglielmo Maria Caporale & Mario Cerrato & Nicola Spagnolo, 2005. "Measuring half-lives: using a non-parametric bootstrap approach," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 1(1), pages 1-4, January.
  3. Hansen,B.E., 1998. "The grid bootstrap and the autoregressive model," Working papers 26, Wisconsin Madison - Social Systems.
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  15. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
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  19. David E. Rapach & Mark E. Wohar, 2004. "The persistence in international real interest rates," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 9(4), pages 339-346.
  20. Jaebeom Kim, 2005. "Convergence Rates to Purchasing Power Parity for Traded and Nontraded Goods: A Structural Error-Correction Model Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 76-86, January.
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Citations

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Cited by:
  1. L. Spierdijk & J.A. Bikker, 2013. "Mean Reversion in Stock Prices: Implications for Long-Term Investors," Working Papers 12-07, Utrecht School of Economics.
  2. repec:ltr:wpaper:2010.06 is not listed on IDEAS
  3. Jae H Kim & Iain Fraser & Rob J. Hyndman, 2010. "Improved Interval Estimation of Long Run Response from a Dynamic Linear Model: A Highest Density Region Approach," Working Papers 2010.06, School of Economics, La Trobe University.
  4. Thabo M. Mokoena & Gupta, R. & Van Eyden, R., 2009. "Half-Life Deviations from PPP in the South African Development Community (SADC)," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
  5. Park, Yung Chul & Park, Hail, 2014. "Stock Market Co-Movement and Exchange Rate Flexibility: Experience of the Republic of Korea," ADBI Working Papers 479, Asian Development Bank Institute.
  6. Jayasuriya, Sisira & Kim, Jae H. & Kumar, Parmod, 2007. "International and Internal Market Integration in Indian agriculture: A study of the Indian Rice Market," 106th Seminar, October 25-27, 2007, Montpellier, France 7935, European Association of Agricultural Economists.
  7. Qian Chen & David E. Giles, 2007. "A Saddlepoint Approximation to the Distribution of the Half-Life Estimator in an Autoregressive Model: New Insights Into the PPP Puzzle," Econometrics Working Papers 0703, Department of Economics, University of Victoria.
  8. Kim, Jae H. & Ji, Philip Inyeob, 2011. "Mean-reversion in international real interest rates," Economic Modelling, Elsevier, vol. 28(4), pages 1959-1966, July.

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