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 squares estimation of the long memory parameter for fractionally differenced processes. We suggest that the general idea of using wavelets for estimating long memory could be used for the estimation of long memory in time series perturbed by noise. One prominent example thereof is the time series of log-Garman-Klass estimates of log volatility of financial markets. The estimator of Percival and Walden (2002) is biased if the long memory time series is perturbed by noise. We propose a new estimator of the long memory parameter 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 the proposed estimator via Monte Carlo simulations. The results show that the estimator may be useful for the estimation of the long memory in volatility.