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September 10, 2025

Simultaneous Detection of Structural Breaks and Outliers in Time Series

Key Points

The proposed method successfully identifies structural breaks and outliers in nonstationary time series data.
Using the minimum description length principle, the study optimizes piecewise autoregressive segment configurations.
A genetic algorithm efficiently finds optimal solutions across numerous configurations, enhancing effective modeling.
The findings imply that integrating outlier detection can significantly improve time series analysis outcomes.

Abstract

ABSTRACT This article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive (AR) processes in the presence of outliers. The number and locations of the piecewise AR segments, as well as the orders of the respective AR processes, are assumed to be unknown. In addition, each piece may contain an unknown number of innovational and/or additive outliers. The minimum description length (MDL) principle is applied to compare various segmented AR fits to the data. The goal is to find the “best” combination of the number of segments, the lengths of the segments, the orders of the piecewise AR processes, and the number and type of outliers. Such a “best” combination is implicitly defined as the optimizer of an MDL criterion. Since the optimization is carried over a large number of configurations of segments and positions of outliers, a genetic algorithm is used to find optimal or near‐optimal solutions. Numerical results from simulation experiments and real data analyses show that the procedure enjoys excellent empirical properties.

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