Data-driven local polynomial for the trend and its derivatives in economic time series

摘要

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.