Nonparametric Forecasting in Time Series—A Comparative Study

Abstract

The problem of predicting a future value of a time series is considered in this article. If the series follows a stationary Markov process, this can be done by nonparametric estimation of the autoregression function. Two forecasting algorithms are introduced. They only differ in the nonparametric kernel-type estimator used: the Nadaraya-Watson estimator and the local linear estimator. There are three major issues in the implementation of these algorithms: selection of the autoregressor variables, smoothing parameter selection, and computing prediction intervals. These have been tackled using recent techniques borrowed from the nonparametric regression estimation literature under dependence. The performance of these nonparametric algorithms has been studied by applying them to a collection of 43 well-known time series. Their results have been compared to those obtained using classical Box-Jenkins methods. Finally, the practical behavior of the methods is also illustrated by a detailed analysis of two data sets.