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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130940In 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.to appear in the Journal of Time Series AnalysisStatistics TheoryAMS Keywords: 62M10, 60G18 Secondary: 62M15On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parametertext