Sequential Outlier Detection in Non-Stationary Time Series

TL;DR

This paper introduces a new sequential outlier detection method for non-stationary time series that controls error rates using extreme value theory, with proven asymptotic properties and validated through simulations.

Contribution

It presents a novel outlier detection approach that addresses multiple testing issues in non-stationary data, with theoretical analysis and empirical comparison to existing methods.

Findings

The method effectively controls error probabilities in sequential testing.

Asymptotic properties are established under null and alternative hypotheses.

Simulation studies demonstrate competitive performance against recent procedures.

Abstract

A novel method for sequential outlier detection in non-stationary time series is proposed. The method tests the null hypothesis of ``no outlier'' at each time point, addressing the multiple testing problem by bounding the error probability of successive tests, using extreme value theory. The asymptotic properties of the test statistic are studied under the null hypothesis and alternative. The finite sample properties of the new detection scheme are investigated by means of a simulation study, and the method is compared with alternative procedures which have recently been proposed in the statistics and machine learning literature.