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On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter

Eric Moulines·François Roueff·Murad Taqqu
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Abstract

In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt the classical semi-parametric framework introduced by Robinson and his co-authors for estimating the memory parameter of a (possibly) non-stationary process. As an application, we obtain minimax upper bounds for the log-scale regression estimator of the memory parameter for a Gaussian process and we derive an explicit expression of its variance.

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Eric Moulines, François Roueff, Murad Taqqu. 2006-08-17. On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter. https://arxiv.org/abs/math/0512635

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