On the Improvements of Metaheuristic Optimization-Based Strategies for Time Series Structural Break Detection

Abstract

Structural break detection is an important time series analysis task. It can be treated as a multi-objective optimization problem, in which we ought to find a time series segmentation such that time series theoretical models constructed on each segment are well-fitted and the segments are long enough to bear meaningful information. Metaheuristic optimization can help us solve this problem. This paper introduces a suite of new cost functions for the structural break detection task. We demonstrate that the new cost functions allow for achieving quantitatively better precision than the cost functions employed in the literature of this domain. We show particular advantages of each new cost function. Furthermore, the paper promotes the use of Particle Swarm Optimization (PSO) in the domain of structural break detection, which so far has relied on the Genetic Algorithm (GA). Our experiments show that PSO outperforms GA for many analysed time series examples. Last but not least, we introduce a non-trivial generalization of the top-performing state-of-the-art approach to the structural break detection problem based on the Minimum Description Length (MDL) rule with autoregressive (AR) model to MDL ARIMA (autoregressive integrated moving average) model.