Monitoring Procedures to Detect Unit Roots and Stationarity

Ansgar Steland

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arXiv · 1001.1831

Monitoring Procedures to Detect Unit Roots and Stationarity

Ansgar Steland

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Abstract

When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical tests for that problem are well studied in the literature. In this paper we provide first results for the problem to monitor sequentially a time series. Our stopping times are based on a sequential version of a kernel-weighted variance-ratio statistic. The asymptotic distributions are established for I(1) processes, a rich class of stationary processes, possibly affected by local nonpara- metric alternatives, and the local-to-unity model. Further, we consider the two interesting change-point models where the time series changes its behaviour after a certain fraction of the observations and derive the associated limiting laws. Our Monte-Carlo studies show that the proposed detection procedures have high power when interpreted as a hypothesis test, and that the decision can often be made very early.

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Ansgar Steland. 2010-01-12. Monitoring Procedures to Detect Unit Roots and Stationarity. https://arxiv.org/abs/1001.1831

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