On asymptotically optimal wavelet estimation of trend functions under long-range dependence

Details On asymptotically optimal wavelet estimation of trend functions under long-range dependence On asymptotically optimal wavelet estimation of trend functions under long-range dependence

2012-03-02

arxiv.org/abs/1203.0392v1

Bernoulli 2012, Vol. 18, No. 1, 137-176

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ332 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ332

We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and resolution parameters are derived. Due to adaptation to the properties of the underlying trend function, the approach shows very good performance for smooth trend functions while remaining competitive with minimax wavelet estimation for functions with discontinuities. Simulations illustrate the asymptotic results and finite-sample behavior.

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