Detection of change points in time series using nonlinear spatio-temporal dynamics.

In ecological or climatological time series, as well as in other areas, it is important to detect change points in which there is a sudden change in some property of the series. In the context of ecology, for instance, those changes represent regime shifts in the ecosystem and can have profound implications for the life of the species in it. A change point can be determined by changes in the mean value of the time series, its variance, power spectrum, or other properties. The changes in the mean value are the most relevant and studied case. Sometimes change points cannot be easily detected by measuring relevant variables of an ecosystem since they can be masked by the noise in the measured variables. Several methods to detect such changes have been developed, some of them require parameters to be adjusted or to make assumptions over the data such as the distribution of the noise or the existence of a single change point in the data series. We introduce a new method to detect change points in the mean value of a time series based on the use of the Ginzburg-Landau equation forced with the data series. The interplay between nonlinearity and diffusion allows for the detection of sudden jumps in the time series while filtering out the noise. We also discuss the robustness in the detection of such point.

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