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Nonparametric estimation of a periodic sequence in the presence of a smooth trend

Authors: Oliver Linton and Michael Vogt
Date: 12 September 2012
Type: cemmap Working Paper, CWP23/12
DOI: 10.1920/wp.cem.2012.2312


In this paper, we study 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 as well as the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study that investigates the small sample behaviour of our procedure. Finally, we illustrate our method by applying it to a series of global temperature anomalies.

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Now published:
Oliver Linton and Michael Vogt March 2014, Nonparametric estimation of a periodic sequence in the presence of a smooth trend, Journal article, Oxford University Press

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