Bernoulli

  • Bernoulli
  • Volume 18, Number 1 (2012), 137-176.

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

Jan Beran and Yevgen Shumeyko

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Abstract

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.

Article information

Source
Bernoulli, Volume 18, Number 1 (2012), 137-176.

Dates
First available in Project Euclid: 20 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1327068621

Digital Object Identifier
doi:10.3150/10-BEJ332

Mathematical Reviews number (MathSciNet)
MR2888702

Zentralblatt MATH identifier
1235.62124

Keywords
long-range dependence mean integrated squared error nonparametric regression thresholding trend estimation wavelet

Citation

Beran, Jan; Shumeyko, Yevgen. On asymptotically optimal wavelet estimation of trend functions under long-range dependence. Bernoulli 18 (2012), no. 1, 137--176. doi:10.3150/10-BEJ332. https://projecteuclid.org/euclid.bj/1327068621


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