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

Oliver Linton and Michael Vogt
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Michael Vogt: Institute for Fiscal Studies

No CWP23/12, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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.

Keywords: Nonparametric estimation; penalized least squares; periodic sequence; temperature anomaly data. (search for similar items in EconPapers)
Date: 2012-09-12
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Journal Article: Nonparametric estimation of a periodic sequence in the presence of a smooth trend (2014)
Working Paper: Nonparametric estimation of a periodic sequence in the presence of a smooth trend (2012)
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