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 stationary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This article 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 that implies a central limit theorem for the control chart. The finite sample properties are investigated by a simulation study.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 9 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.