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Half-life estimation based on the bias-corrected bootstrap: A highest density region approach

  • Kim, Jae H.
  • Silvapulle, Param
  • Hyndman, Rob J.

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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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 51 (2007)
Issue (Month): 7 (April)
Pages: 3418-3432

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Handle: RePEc:eee:csdana:v:51:y:2007:i:7:p:3418-3432
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  1. Jeremy Berkowitz & Lutz Kilian, . "Recent Developments in Bootstrapping Time Series," Finance and Economics Discussion Series 1996-45, Board of Governors of the Federal Reserve System (U.S.).
  2. Campbell, John & Mankiw, Gregory, 1987. "Are Output Fluctuations Transitory?," Scholarly Articles 3122545, Harvard University Department of Economics.
  3. 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.
  4. Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-93, October.
  5. Guglielmo Maria Caporale & Mario Cerrato & Nicola Spagnolo, 2004. "Measuring Half-Lives Using A Non-Parametric Bootstrap Approach," Economics and Finance Discussion Papers 04-13, Economics and Finance Section, School of Social Sciences, Brunel University.
  6. Nikolay Gospodinov, 2004. "Asymptotic confidence intervals for impulse responses of near-integrated processes," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 505-527, December.
  7. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
  8. Hansen,B.E., 1998. "The grid bootstrap and the autoregressive model," Working papers 26, Wisconsin Madison - Social Systems.
  9. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
  10. Kilian, Lutz & Gonçalves, Sílvia, 2002. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Discussion Paper Series 1: Economic Studies 2002,26, Deutsche Bundesbank, Research Centre.
  11. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  12. Rossi, Barbara, 2002. "Confidence Intervals for Half-life Deviations from Purchasing Power Parity," Working Papers 02-08, Duke University, Department of Economics.
  13. Christian Murray & David Papell, 2005. "The purchasing power parity puzzle is worse than you think," Empirical Economics, Springer, vol. 30(3), pages 783-790, October.
  14. Emmanuel Flachaire, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00175910, HAL.
  15. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  16. 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.
  17. Godfrey, L.G., 2006. "Tests for regression models with heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2715-2733, June.
  18. Campbell, John Y. & Mankiw, N. Gregory, 1989. "International evidence on the persistence of economic fluctuations," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 319-333, March.
  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. Lutz Kilian & Tao Zha, 2002. "Quantifying the uncertainty about the half-life of deviations from PPP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 107-125.
  21. 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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