Reversed Residuals in Autoregressive Time Series Analysis

摘要

Both linear and nonlinear time series can have directional features, featureswhich indicate that the series do not maintain identical statistical properties when the direction on the time scale is reversed. The main purpose of the present paper is to develop the analysis of these features and to indicate and illustrate how they can be used for the investigation and modelling of linear or nonlinear autoregressive statistical models. In particular, the aim of the paper is to introduce the idea of reversed residuals and to develop some of their properties. Particular pairs of reversed and ordinary residuals are shown to produce partial autocorrelation coefficients: quadratic types of partial autocorrelation coefficients are introduced to assess dependence associated with nonlinear models which nevertheless have linear autoregressive (Yule-Walker) correlation structures. (kr)