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

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

2005-12-29

arxiv.org/abs/math/0512635v2

Mathematics

Statistics Theory

to appear in the Journal of Time Series Analysis

Scientific paper

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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