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

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Author Info
Jae Kim ()
Param Silvapulle ()
Rob J. Hyndman ()

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

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. G. S. Hongyi Li, 1996. "Bootstrapping time series models," Econometric Reviews, Taylor and Francis Journals, vol. 15(2), pages 115-158. [Downloadable!] (restricted)
  5. Rossi, Barbara, 2002. "Confidence Intervals for Half-life Deviations from Purchasing Power Parity," Working Papers 02-08, Duke University, Department of Economics. [Downloadable!]
    Other versions:
  6. Christian J. Murray & David H. Papell, 2000. "The Purchasing Power Parity Persistence Paradigm," Econometric Society World Congress 2000 Contributed Papers 0017, Econometric Society. [Downloadable!]
    Other versions:
  7. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November. [Downloadable!] (restricted)
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  8. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June. [Downloadable!] (restricted)
  9. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November. [Downloadable!] (restricted)
  10. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November. [Downloadable!] (restricted)
    Other versions:
  11. 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. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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  14. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. John Y. Campbell & N. Gregory Mankiw, 1989. "International Evidence on the Persistence of Economic Fluctuations," NBER Working Papers 2498, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. 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. [Downloadable!]
  18. 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.
  19. 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. [Downloadable!]
  20. 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.
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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