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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.

Suggested Citation

  • Jae Kim & Param Silvapulle & Rob J. Hyndman, 2006. "Half-Life Estimation based on the Bias-Corrected Bootstrap: A Highest Density Region Approach," Monash Econometrics and Business Statistics Working Papers 11/06, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2006-11
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp11-06.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    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.
    2. 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).
    3. Kim, Jae H. & Fraser, Iain & Hyndman, Rob J., 2011. "Improved interval estimation of long run response from a dynamic linear model: A highest density region approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2477-2489, August.
    4. repec:eee:intfin:v:50:y:2017:i:c:p:36-51 is not listed on IDEAS
    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. L. Spierdijk & J.A. Bikker, 2012. "Mean Reversion in Stock Prices: Implications for Long-Term Investors," Working Papers 12-07, Utrecht School of Economics.
    7. Georgios Loukopoulos & Dimitrios Antonopoulos, 2015. "Purchasing Power Parity: A Unit Root, Cointegration and VAR Analysis in Emerging and Advanced Countries," Business and Economic Research, Macrothink Institute, vol. 5(1), pages 262-279, June.
    8. 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.
    9. Kim, Jae H. & Ji, Philip Inyeob, 2011. "Mean-reversion in international real interest rates," Economic Modelling, Elsevier, vol. 28(4), pages 1959-1966, July.

    More about this item

    Keywords

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

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications

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