Wavelets and Estimation of Long Memory in Log Volatility and Time Series Perturbed by Noise

Percival and Walden (2002) present a wavelet methodology of the least squaresestimation of the long memory parameter for fractionally differenced processes. Wesuggest that the general idea of using wavelets for estimating long memory could beused for the estimation of long memory in time series perturbed by noise. One prominentexample thereof is the time series of log-Garman-Klass estimates of log volatility of fi nan-cial markets. The estimator of Percival and Walden (2002) is biased if the long memorytime series is perturbed by noise. We propose a new estimator of the long memory param-eter which combines (in its construction) the frequency-domain approach of Sun & Phillips(2003) and the approach of Percival & Walden (2002). We illustrate the properties of theproposed estimator via Monte Carlo simulations. The results show that the estimator maybe useful for the estimation of the long memory in volatility.