Genetic algorithm with a Bayesian approach for the detection of multiple points of change of time series of counting exceedances of specific thresholds

The change-point detection problem has been widely studied in time series and signal processing literature. The current methods can be resumed in the search for the appropiate partitions of a whole time series such that the problem can be approached as one of optimization; nevertheless, an exact optimization approach could result computationally expensive and approximate ones discard potential scenarios for change-points configurations in a non-rigorous manner. Thus, a framework it is presented to detect change-points in a univariate time series using a decision criterion based on the Minimum Description Length (MDL), modified such that a Bayesian analysis is included. To search for the points of change, the times where mean value deviations occur (exceedances) are analyzed and then it is evaluated which of these could constitute a change-point through a genetic algorithm using as a fitness function the previously described MDL. The effectiveness of the method it is assessed through a simulation study and on the other hand, it is analyzed its practical validity in a real dataset for the presence of Particulate Matter of less than 2.5 microns (PM2.5) in Bogot\'a, Colombia for the 2018-2020 period under different settings to understand the algorithm convergence. It is found that this definition for the objective function tends to find better results for both the number of change-points and their location in the series for most of cases reducing the error in comparison to other available methods in the literature.