Abstract
We investigate the performance of several wavelet-based estimators of the fractional difference parameter. We consider situations where, in addition to long-range dependence, the time series exhibit heavy tails and are perturbed by polynomial and change-point trends. We make detailed study of a wavelet-domain pseudo Maximum Likelihood Estimator (MLE), for which we provide an asymptotic and finite-sample justification. Using numerical experiments, we show that unlike the traditional time-domain estimators, estimators based on the wavelet transform are robust to additive trends and change points in mean, and produce accurate estimates even under significant departures from normality. The Wavelet-domain MLE appears to dominate a regression-based wavelet estimator in terms of smaller root mean squared error. These findings are derived from a simulation study and application to computer traffic traces.
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Research supported by NSF grant DMS-0413653.
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Jach, A., Kokoszka, P. Robust Wavelet-Domain Estimation of the Fractional Difference Parameter in Heavy-Tailed Time Series: An Empirical Study. Methodol Comput Appl Probab 12, 177–197 (2010). https://doi.org/10.1007/s11009-008-9105-3
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DOI: https://doi.org/10.1007/s11009-008-9105-3