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Nonparametric Estimation of a Periodic Sequence in the Presence of a Smooth Trend

Saturday 1st March 2014
Biometrika
Vogt, M. and Linton, O.
We investigate a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates and the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study and an application to global temperature anomaly data.
Keywords
Nonparametric estimation
Penalized least squares
Periodic sequence
Temperature anomaly data.
Themes
empirical
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