Nonparametric estimation of a periodic sequence in the presence of a smooth trend
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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- Robert M. De Jong & James Davidson, 2000.
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2008-37, School of Economics and Management, University of Aarhus.
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- Peter Hall & Ming Li, 2006. "Using the periodogram to estimate period in nonparametric regression," Biometrika, Biometrika Trust, vol. 93(2), pages 411-424, June.
- Marc G. Genton & Peter Hall, 2007. "Statistical inference for evolving periodic functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 643-657.
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