Abstract
Wavelet methods are used to estimate density and (auto-) regression functions that are possibly discontinuous. For stationary time series that satisfy appropriate mixing conditions, we derive mean integrated squared errors (MISEs) of wavelet-based estimators. In contrast to the case for kernel methods, the MISEs of wavelet-based estimators are not affected by the presence of discontinuities in the curves. Applications of this approach to problems of identification of nonlinear time series models are discussed.
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Truong, Y.K., Patil, P.N. Asymptotics for Wavelet Based Estimates of Piecewise Smooth Regression for Stationary Time Series. Annals of the Institute of Statistical Mathematics 53, 159–178 (2001). https://doi.org/10.1023/A:1017928823619
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DOI: https://doi.org/10.1023/A:1017928823619