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

39 Pages Posted: 13 Sep 2012

See all articles by Michael Vogt

Michael Vogt

University of Cambridge

Oliver B. Linton

University of Cambridge

Date Written: September 11, 2012


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 sequenc, temperature anomaly data

JEL Classification: C12

Suggested Citation

Vogt, Michael and Linton, Oliver B., Nonparametric Estimation of a Periodic Sequence in the Presence of a Smooth Trend (September 11, 2012). Available at SSRN: or

Michael Vogt

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

Oliver B. Linton (Contact Author)

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

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