Nonparametric monitoring of time series to detect stationarity and unit roots
by
Ansgar Steland
Institute of Statistics, RWTH Aachen University

An important issue of the sequential analysis of time series is

the problem to detect stationarity and unit roots, respectively.

Whereas classic hypothesis tests for that problem are well studied,

sequential results are more recent.

In this talk we study appropriate stopping times and the underlying

stochastic processes. Our (functional) central limit theorems

work under general assumptions which allow for conditional

heteroskedasticity. Particularly, we derive the asymptotic laws

under the assumption that the time series has an unit root.

We also consider the case that the time series has a deterministic (polynomial) trend component.

Here procedures may be based on sequentially updated residuals.

Simulation studies indicate that the procedures work well.

Date received: April 19, 2007