Curve estimation for locally stationary time series models

Abstract

This chapter describes curve estimation for locally stationary time series models. Locally stationary processes are models for nonstationary time series whose behavior can locally be approximated by a stationary process. In this situation, the classical characteristics of the process, such as the covariance function at some lag, the spectral density at some frequency, or for example the parameters of a process are curves which change slowly over time. The properties of methods for stationary models are usually well investigated. This has mainly been done in asymptotic considerations by using such powerful results as the ergodic theorem, or the central limit theorem for stationary mixing sequences or martingale differences. The existence of such tools for asymptotic considerations has lead over, the last decades, to an overemphasis of stationary models while in practice many time series show a nonstationary behavior. It is found that the simplest way to do inference for locally stationary processes is through stationary methods on segments. A data adaptive segment choice is derived by a plug-in strategy.