Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models
Abstract
The question whether a time series behaves as a random walk or as a station- ary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This paper studies the problem to detect sequentially that the error terms in a polynomial regression model no longer behave as a random walk but as a stationary process. We provide the asymptotic distribution theory for a monitoring procedure given by a control chart, i.e., a stopping time, which is related to a well known unit root test statistic calculated from sequentially updated residuals. We provide a functional central limit theorem for the corresponding stochastic process which implies a central limit theorem for the control chart. The finite sample properties are investigated by a simulation study.
Keywords
Cite
@article{arxiv.1001.1845,
title = {Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models},
author = {Ansgar Steland},
journal= {arXiv preprint arXiv:1001.1845},
year = {2010}
}