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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 infinancial statistics, econometrics, and engineering. This paper studies theproblem to detect sequentially that the error terms in a polynomial regressionmodel no longer behave as a random walk but as a stationary process. We providethe asymptotic distribution theory for a monitoring procedure given by acontrol chart, i.e., a stopping time, which is related to a well known unitroot test statistic calculated from sequentially updated residuals. We providea functional central limit theorem for the corresponding stochastic processwhich implies a central limit theorem for the control chart. The finite sampleproperties are investigated by a simulation study.

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