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Real-world systems are often complex, dynamic, and nonlinear. Understandingthe dynamics of a system from its observed time series is key to the predictionand control of the system's behavior. While most existing techniques tacitlyassume some form of stationarity or continuity, abrupt changes, which are oftendue to external disturbances or sudden changes in the intrinsic dynamics, arecommon in time series. Structural breaks, which are time points at which thestatistical patterns of a time series change, pose considerable challenges todata analysis. Without identification of such break points, the same dynamicrule would be applied to the whole period of observation, whereas falseidentification of structural breaks may lead to overfitting. In this paper, wecast the problem of decomposing a time series into its trend and seasonalcomponents as an optimization problem. This problem is ill-posed due to thearbitrariness in the number of parameters. To overcome this difficulty, wepropose the addition of a penalty function (i.e., a regularization term) thataccounts for the number of parameters. Our approach simultaneously identifiesseasonality and trend without the need of iterations, and allows the reliabledetection of structural breaks. The method is applied to recorded data on fishpopulations and sea surface temperature, where it detects structural breaksthat would have been neglected otherwise. This suggests that our method canlead to a general approach for the monitoring, prediction, and prevention ofstructural changes in real systems.

Detecting structural breaks in seasonal time series by regularized optimization