Nonparametric Estimation of a Periodic Sequence in the Presence of a Smooth Trend
Nonparametric Estimation of a Periodic Sequence in the Presence of a Smooth Trend
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DOI：
10.2139/ssrn.2144996
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发表时间：
2012-09
期刊：
影响因子：
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通讯作者：
M. Vogt;O. Linton
中科院分区：
文献类型：
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作者：
M. Vogt;O. Linton
本文研究了一类含有周期分量、光滑趋势函数和随机误差项的非参数回归模型。我们提出了一个程序来估计未知的周期和周期分量的函数值以及非参数趋势函数。本文的理论部分建立了我们的估计的渐近性质。特别是，我们表明，我们的估计的周期是一致的。此外，我们还得到了周期分量和趋势函数的估计量的收敛速度和极限分布。的渐近结果补充了模拟研究，调查我们的程序的小样本行为。最后，我们说明了我们的方法，将其应用到一系列的全球温度异常。
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.