On Local Trigonometric Regression Under Dependence

Jan Beran, Britta Steffens and Sucharita Ghosh

Journal of Time Series Analysis, 2018, vol. 39, issue 4, 592-617

Abstract: 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.

Date: 2018
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