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This paper presents a framework for detecting changes in non-linear dynamics for time series based on the theory of KM2O-Langevin equations. This paper has two contributions one is to define the pseudo determinacy function that deduces the non-linear dynamics behind the subsequences of the time series data the other is to define the distance of dynamics between the subsequences by the pseudo determinacy function to understand how and when the non-linear dynamics changes. In contrast to the existing methods such as Singular-Spectrum Analysis and Recurrence Quantification Analysis the proposed method can distinguish the difference between a temporal outlier and a change in non-linear dynamics. Moreover, applying the proposed method to the real data, we found the indirect relation between the change in non-linear dynamics and some outer force (the actress in TV commercial or attack by competitors).

Detection of changes in non-linear dynamics for time series based on the theory of KM2O-Langevin equations