On Local Trigonometric Regression Under Dependence |
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Authors: | Jan Beran Britta Steffens Sucharita Ghosh |
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Affiliation: | 1. Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany;2. Statistics Lab, Swiss Federal Research Institute WSL, Birmensdorf, Switzerland |
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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. |
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Keywords: | seasonal smoothing time series decomposition local trigonometric regression long‐range dependence |
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