An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets

✍ Scribed by Mark J. Jensen

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 222 KB
• Volume: 24
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(99)00010-x

✦ Synopsis

In this paper we apply compactly supported wavelets to the ARFIMA(p, d, q) longmemory process to develop an alternative maximum likelihood estimator of the di!erencing parameter, d, that is invariant to unknown means, model speci"cation, and contamination. We show that this class of time series have wavelet transforms whose 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 matrix equal to the covariance matrix except with the o!-diagonal elements set equal 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 di!erencing parameter to a variety of compactly supported wavelets, series length, and contamination levels by generating ARFIMA(p, d, q) processes for di!erent values of p, d, and q, and calculating the wavelet MLE using only the main diagonal elements of its covariance matrix. In our simulations we "nd the wavelet MLE to be superior to the approximate frequency 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 "nd the wavelet MLE to be robust to model speci"cation and as such is an attractive alternative semiparameter estimator to the Geweke, Porter}Hudak estimator.