ABSTRACT The main purpose of this paper is the development of data-driven iterative plug-in algorithms for local polynomial estimation of the trend and its derivatives under dependent errors. Furthermore, a data-driven lag-window estimator for the variance factor in the bandwidth is proposed so that the nonparametric stage is carried out without any parametric assumption on the stationary errors. Analysis of the residuals using an ARMA model is further discussed. Moreover, some computational features of the data-driven algorithms are discussed in detail. Practical performance of the proposals is confirmed by a simulation study and a comparative study, and illustrated by quarterly US GDP and labour force data. An R package called ‘smoots’ (smoothing time series) for smoothing the trend and its derivatives in short-memory time series is developed based on the proposals of this paper.

中文翻译：

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经济时间序列趋势及其导数的数据驱动局部多项式

摘要 本文的主要目的是开发数据驱动的迭代插件算法，用于在相关误差下对趋势及其导数进行局部多项式估计。此外，提出了用于带宽中方差因子的数据驱动的滞后窗口估计器，以便在没有对平稳误差进行任何参数假设的情况下执行非参数阶段。进一步讨论了使用 ARMA 模型的残差分析。此外，详细讨论了数据驱动算法的一些计算特征。模拟研究和比较研究证实了这些建议的实际表现，并以美国季度 GDP 和劳动力数据说明。