Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models

Details Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models

2010-01-12

arxiv.org/abs/1001.1845v1

Sequential Analysis 2008, 27 (3), 304-329

Mathematics

Probability

Scientific paper

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.

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