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On Local Trigonometric Regression Under Dependence


  • Jan Beran
  • Britta Steffens
  • Sucharita Ghosh


We consider nonparametric estimation of an additive time series decomposition into a long†term trend μ and a smoothly changing seasonal component S under general assumptions on the dependence structure of the residual process. The rate of convergence of local trigonometric regression estimators of S turns out to be unaffected by the dependence, even though the spectral density of the residual process has a pole at the origin. In contrast, the rate of convergence of nonparametric estimators of μ depends on the long†memory parameter d. Therefore, in the presence of long†range dependence, different bandwidths for estimating μ and S should be used. A data adaptive algorithm for optimal bandwidth choice is proposed. Simulations and data examples illustrate the results.

Suggested Citation

  • Jan Beran & Britta Steffens & Sucharita Ghosh, 2018. "On Local Trigonometric Regression Under Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(4), pages 592-617, July.
  • Handle: RePEc:bla:jtsera:v:39:y:2018:i:4:p:592-617

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