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

TL;DR

This paper introduces a robust wavelet-based log-periodogram method for estimating long-memory parameters in stochastic volatility models, outperforming classical estimators especially under non-Gaussian noise conditions.

Contribution

It combines wavelet multi-resolution analysis with LAD-based robust periodogram estimation to improve long-memory parameter estimation in noisy, non-Gaussian time series.

Findings

Outperforms GPH and WBLP estimators in simulations

Reduces mean squared error across various scenarios

Effective in non-Gaussian noise environments

Abstract

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 (LAD) 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 Porter-Hudak (GPH) and Wavelet-Based Log-Periodogram (WBLP) estimators, particularly in terms of mean squared error, across various sample sizes and parameter configurations.