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The Empirical Properties of Some Popular Estimators of Long Memory Processes

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We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, H, or the fractional integration parameter, d, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally integrated series with lengths between 100 and 10,000 data points and H values between 0.55 and 0.90 or d values between 0.05 and 0.40. We apply all 12 estimators to the Campito Mountain data and estimate the accuracy of their estimates using the Beran goodness of t test for long memory time series.

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  • Jennifer Brown & Les Oxley & William Rea & Marco Reale, 2008. "The Empirical Properties of Some Popular Estimators of Long Memory Processes," Working Papers in Economics 08/13, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:08/13
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/0813.pdf
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    1. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, University Library of Munich, Germany.
    2. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    3. Baillie, Richard T. & Chung, Sang-Kuck, 2002. "Modeling and forecasting from trend-stationary long memory models with applications to climatology," International Journal of Forecasting, Elsevier, vol. 18(2), pages 215-226.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    5. John Haslett & Adrian E. Raftery, 1989. "Space‐Time Modelling with Long‐Memory Dependence: Assessing Ireland's Wind Power Resource," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 1-21, March.
    6. Deo, Rohit S. & Chen, Willa W., 2000. "On the integral of the squared periodogram," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 159-176, January.
    7. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    8. Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 1999. "Variance-type estimation of long memory," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 1-24, March.
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    Cited by:

    1. Chow, Ying-Foon & Lam, James T.K. & Yeung, Hinson S., 2009. "Realized volatility of index constituent stocks in Hong Kong," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2809-2818.
    2. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
    3. Michael McAleer & Felix Chan & Les Oxley, 2013. "Modeling and Simulation: An Overview," Working Papers in Economics 13/18, University of Canterbury, Department of Economics and Finance.
    4. Les Oxley & Chris Price & William Rea & Marco Reale, 2008. "A New Procedure to Test for H Self-Similarity," Working Papers in Economics 08/16, University of Canterbury, Department of Economics and Finance.

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    More about this item

    Keywords

    Strong dependence; global dependence; long range dependence; Hurst parameter estimators;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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