Estimating the Long-Memory Parameter in Nonstationary Processes Using Wavelets

In this article, we propose two new semiparametric estimators in the wavelet domain in order to estimate the parameter of nonstationary long memory models. Compared to the Fourier transform, the advantage of the wavelet approach to analyze the behavior of nonstationary time series is that it can localize a process simultaneously in time and scale. We thus develop a Wavelet Exact Local Whittle estimator and a Wavelet Feasible Exact Local Whittle estimator, which extend the estimators of Phillips and Shimotsu (Ann Stat 32(2):656–692, <CitationRef CitationID="CR16">2004</CitationRef>), Shimotsu and Phillips (Ann Stat 33(4):1890–1933, <CitationRef CitationID="CR20">2005</CitationRef>; J Econom 130:209–233, <CitationRef CitationID="CR21">2006</CitationRef>) and Shimotsu (Econom Theory 26(2):501–540, <CitationRef CitationID="CR19">2010</CitationRef>) into the wavelet domain. Simulation experiments show that the new estimators perform better under most situations in the stationary and nonstationary cases. We also applied these two new semiparametric estimators to some financial series (daily stock market indices and exchange rates). Copyright Springer Science+Business Media New York 2013