Wavelet-based estimation of long-memory parameter in stochastic volatility models using a robust log-periodogram

In this paper, we propose a novel method for estimating the long-memory parameter in time series. By combining the multi-resolution framework of wavelets with the robustness of the least absolute deviations criterion, we introduce a periodogram providing a robust alternative to classical methods in the presence of non-Gaussian noise. Incorporating this periodogram into a log-periodogram regression, we develop a new estimator. Simulation studies demonstrate that our estimator outperforms the Geweke and PorterHudak (GPH) and wavelet-based log-periodogram (WBLP) estimators, particularly in terms of mean squared error, across various sample sizes and parameter configurations.