Tests of Correlation Among Wavelet-Based Estimates for Long Memory Processes

Abstract

Long memory models have received a significant amount of attention in the theoretical literature as they cover a wide range of applications, including economics and telecommunications. In recent years, a semiparametric estimator of the long memory parameter of stationary processes with long-range dependence, based on wavelet decomposition, has been proposed and studied by Veitch and Abry (1999) under the idealized assumption of decorrelation among wavelet coefficients. The asymptotic statistical analysis of the wavelet-based estimator has been recently complemented taking into account the correlations among wavelet coefficients, at fixed scales as well as among different scales (Bardet et al., 2000). The goal of the present article is to study the statistical properties of the wavelet-based estimator for a finite sample size and the correlation among the wavelet-based long memory estimates. The analysis is conducted by simulation, through the use of the circulant matrix method and shows that the correlation among wavelet coefficients has an impact on the moments of the wavelet-based estimator and on the correlation among the wavelet-based long memory estimates computed on non overlapping blocks of the original process.