An Approximate Wavelet MLE of Short and Long Memory Parameters
AbstractBy 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.
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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 9802003.
Length: 23 pages
Date of creation: 16 Feb 1998
Date of revision: 21 Jun 1999
Note: Type of Document - PostScript; prepared on LaTeX Sun Ultra 1; to print on PostScript; pages: 23 ; figures: included
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Long Memory; Fractional Integration; ARFIMA; Wavelets;
Other versions of this item:
- Jensen Mark J., 1999. "An Approximate Wavelet MLE of Short- and Long-Memory Parameters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-17, January.
- Mark J. Jensen, 1999. "An Approximate Wavelet MLE of Short- and Long-Memory Parameters," Computing in Economics and Finance 1999 1243, Society for Computational Economics.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-1998-10-02 (All new papers)
- NEP-ECM-1998-10-02 (Econometrics)
- NEP-ETS-1998-10-02 (Econometric Time Series)
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