An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets
AbstractIn 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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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 9709002.
Length: 31 pages
Date of creation: 30 Sep 1997
Date of revision:
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
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ARFIMA; Fractional Integration; Long-memory; MLE; Wavelets;
Other versions of this item:
- Jensen, Mark J., 2000. "An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 361-387, March.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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