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On Local Trigonometric Regression Under Dependence
Author(s) -
Beran Jan,
Steffens Britta,
Ghosh Sucharita
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12287
Subject(s) - mathematics , estimator , residual , rate of convergence , nonparametric statistics , nonparametric regression , trigonometry , bandwidth (computing) , regression , convergence (economics) , econometrics , statistics , algorithm , mathematical analysis , computer science , computer network , channel (broadcasting) , economics , economic growth
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.