Detecting smooth changes in locally stationary processes

Abstract

In a wide range of applications, the stochastic properties of the observed time series change over time. It is often realistic to assume that the properties are approximately the same over short time periods and then gradually start to vary. This behaviour is well modelled by locally stationary processes. In this paper, we investigate the question how to estimate time spans where the stochastic features of a locally stationary time series are the same. We set up a general method which allows to deal with a wide variety of features including the mean, covariances, higher moments and the distribution of the time series under consideration. In the theoretical part of the paper, we derive the asymptotic properties of our estimation method. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by an application to financial data.