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An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets

  • Mark J. Jensen

    (University of Missouri - Columbia)

In this paper we apply compactly supported wavelets to the ARFIMA(p,d,q) long-memory process to develop an alternative maximum likelihood estimator of the differencing parameter, d, that is invariant to the unknown mean and model specification, and to the level of contamination. We show that this class of time series have wavelet transforms who's covariance matrix is sparse when the wavelet is compactly supported. It is shown that the sparse covariance matrix can be approximated to a high level of precision by a matix equal to the covariance amtrix except with the off-diagonal elements set to zero. This diagonal matrix is shown to reduce the order of calculating the likelihood function to an order smaller than those associated with the exact MLE method. We test the robustness of the wavelet MLE of the fractional differencing parameter to a variety of compactly supported wavelets, series length, and contamination by generating ARFIMA(p,d,q) processes for different values of p, d, and q and calculating the wavelet MLE estimate using only the main diagonal elements of its covariance matrix. In our simulations we find the wavelet MLE to be superior to the approximate MLE when estimating contaminated ARFIMA(0,d,0), and uncontaminated ARFIMA(1,d,0) and ARFIMA(0,d,1) processes except when the MA parameter is close to one. We also find the wavelet MLE to be robust to model specification and as such is an attractive alternative semiparametric estimator to the Geweke-Hudak estimator.

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Paper provided by EconWPA in its series Econometrics with number 9709002.

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Length: 31 pages
Date of creation: 30 Sep 1997
Date of revision:
Handle: RePEc:wpa:wuwpem:9709002
Note: Type of Document - Postscript File; prepared on Unix Sparc/Latex; to print on Postscript; pages: 31 ; figures: included. Postscript file that contains the figures
Contact details of provider: Web page: http://128.118.178.162

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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, EconWPA.
  2. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  3. Yin-Wong Cheung & Francis X. Diebold, 1990. "On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean," Discussion Paper / Institute for Empirical Macroeconomics 34, Federal Reserve Bank of Minneapolis.
  4. C. M. Schmidt & R. Tschernig, 1995. "The Identification of Fractional ARIMA Models," SFB 373 Discussion Papers 1995,8, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  6. Alex Maynard & Peter C. B. Phillips, 2001. "Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 671-708.
  7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  8. Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264.
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