Sequential Outlier Detection in Non-Stationary Time Series

TL;DR

This work tackles sequential outlier detection in non-stationary time series by casting the problem in a multiple-testing framework and deriving an EVT-based decision rule. It combines a bias-corrected local linear estimator to estimate the nonstationary mean with a residual-based test whose critical values are obtained from a generalized extreme value distribution under alpha-mixing, allowing continuous monitoring without excessive conservatism. Theoretical results establish asymptotic level control and consistency, while extensive simulations and real-world temperature data demonstrate competitive performance against existing methods, particularly in online settings. The approach is well-suited for high-frequency sensor data where dependence and nonstationarity violate iid assumptions, enabling robust and scalable sequential anomaly detection with provable guarantees.

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.

Figures (2)

• Figure 1: Different choices of the mean function $\mu$. Left: $\mu_1$. Center: $\mu_2$, Right: $\mu_3$.
• Figure 2: Temperature data from different Australian locations with marked outliers. Top: Boulia. Bottom: Hobart.

Theorems & Definitions (5)

• Remark 4
• Theorem 5
• Remark 7
• Corollary 8
• Proposition 9