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OLS Estimate of Fractional Differencing Parameter Using Wavelets Derived from Smoothing Kernels

Author

Listed:
  • Mark J. Jensen

    (Southern Illinois University at Carbondale)

Abstract

This paper develops a consistent OLS estimate of a fractionally integrated processes' differencing parameter, using continuous wavelet theory as constructed from smoothing kernels. We show that a log-log linear relationship exists between the variance of the wavelet coefficient and the level at which the fractionally integrated processes is smoothed. This linear relationship occurs because the self-simularity property of the fractionally integrated process and the self-similarity of the wavelet causes the smoothing level to continually appear in the wavelet transformation. Since the wavelet coefficient can be interpreted as the k-th order details of the series at some level of smoothing, we also show that the above log-log relationship can be derived from the variance of the 1-st order derivative of the time series smoothed by a kernel that is well localized in both time and frequency space. Lastly, we derive the asymptotic biasness and variance of the OLS estimate and test our consistent estimate with a number of Monte Carlo experiments.

Suggested Citation

  • Mark J. Jensen, 1995. "OLS Estimate of Fractional Differencing Parameter Using Wavelets Derived from Smoothing Kernels," Econometrics 9506002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:9506002
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    More about this item

    Keywords

    Fractionally Integrated Processes; Long-Memory; Smoothing Kernels; Wavelets;
    All these keywords.

    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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