Wavelet analysis of nonlinear long-range dependent processes. Applications to financial time series

Abstract

We present and study the performance of the semiparametric wavelet estimator for the long-memory parameter devised by [Veitch and Abry (1999)]. We compare this estimator with two semiparametric estimators in the spectral domain, the local Whittle (LW) estimator developed by [Robinson (1995a)] and the log-periodogram (LP) estimator by [Geweke and Porter-Hudak (1983)]. The wavelet estimator performs well for a wide range of nonlinear long-memory processes in the conditional mean and the conditional variance, and is reliable for discriminating between change-points and long-range dependence in volatility. We also address the issue of selection of the range of octaves used as regressors by the weighted least squares estimator. We will see that using the feasible optimal bandwidths for either the LW and LP estimators, respectively studied by [Henry and Robinson (1996) and [Henry (2001)], is a useful rule of thumb for selecting the lowest octave. We apply the wavelet estimator to volatility series of high frequency (intra-day) Foreign Exchange (FX) rates, and to the volatility and volume of stocks of the Dow Jones Industrial Average Index. © 2007 Springer Berlin Heidelberg.