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An Approximate Wavelet MLE of Short and Long Memory Parameters

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  • Mark J. Jensen

    (University of Missouri - Columbia)

Abstract

By design a wavelet's strength rests in its ability to simultaneously localize a process in time-scale space. The wavelet's ability to localize a time series in time-scale space directly leads to the computational efficiency of the wavelet representation of a N X N matrix operator by allowing the N largest elements of the wavelet represented operator to adequately represent the matrix operator. This property allos many dense matrices to have sparse representation when transformed by wavelets. In this paper we generalize the long-memory parameter estimator of McCoy and Walden (1996) to simultaneously estaimte short and long-memory parameters. Using the sparse wavelet representation of a matrix operator, we are able to adequately approximate an ARFIMA models likelihood function with the series wavelet coefficients and their variances. Maximization of this approximate likelihood function over the short and long-memory parameter space results in the approximate wavelet maximum likelihood estimator of the ARFIMA model. By simultaneously maximizing the likelihood function over both the short and long-memory parameters, and using only the wavelet coefficient's variances, the approximate wavelet MLE provides an equally fast alternative to the frequency-domain MLE. Futhermore, the simulation studies reveal the approximate wavelet MLE to be robust over the invertible parameter region of the ARFIMA model's moving average parameter, whereas the frequency-domain MLE dramatically deteriorates as the moving average parameter approaches the boundaries of invertibility.

Suggested Citation

  • Mark J. Jensen, 1998. "An Approximate Wavelet MLE of Short and Long Memory Parameters," Econometrics 9802003, EconWPA, revised 21 Jun 1999.
  • Handle: RePEc:wpa:wuwpem:9802003
    Note: Type of Document - PostScript; prepared on LaTeX Sun Ultra 1; to print on PostScript; pages: 23 ; figures: included
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    References listed on IDEAS

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    11. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
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    Cited by:

    1. Jensen Mark J., 2016. "Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 455-475, September.
    2. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    3. Charfeddine, Lanouar & Guégan, Dominique, 2012. "Breaks or long memory behavior: An empirical investigation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5712-5726.
    4. In, Francis & Kim, Sangbae, 2006. "Multiscale hedge ratio between the Australian stock and futures markets: Evidence from wavelet analysis," Journal of Multinational Financial Management, Elsevier, vol. 16(4), pages 411-423, October.
    5. Charfeddine, Lanouar, 2016. "Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis," Economic Modelling, Elsevier, vol. 53(C), pages 354-374.
    6. Kraicová Lucie & Baruník Jozef, 2017. "Estimation of long memory in volatility using wavelets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    7. repec:bpj:sndecm:v:21:y:2017:i:4:p:18:n:6 is not listed on IDEAS
    8. Boubaker Heni & Canarella Giorgio & Miller Stephen M. & Gupta Rangan, 2017. "Time-varying persistence of inflation: evidence from a wavelet-based approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-18, September.
    9. Kei Nanamiya, 2014. "Modelling For The Wavelet Coefficients Of Arfima Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 341-356, July.
    10. Brandon Whitcher, 2000. "Wavelet-Based Estimation Procedures For Seasonal Long-Memory Models," Computing in Economics and Finance 2000 148, Society for Computational Economics.

    More about this item

    Keywords

    Long Memory; Fractional Integration; ARFIMA; Wavelets;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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