A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Minimum-bandwidth discrete-time wavelets
Signal Processing
Fractal estimation from noisy data via discrete fractional Gaussiannoise (DFGN) and the Haar basis
IEEE Transactions on Signal Processing
Estimation of fractal signals from noisy measurements usingwavelets
IEEE Transactions on Signal Processing
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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, 2004), Shimotsu and Phillips (Ann Stat 33(4):1890---1933, 2005; J Econom 130:209---233, 2006) and Shimotsu (Econom Theory 26(2):501---540, 2010) 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).