The Use of Genetic Algorithm in Clustering of ARMA Time Series

Time series clustering is a well-covered topic in the data mining literature. In this paper, we assume that each of a large number of time series follows one of several autoregressive-moving-average (ARMA) models. We propose to jointly assign time series to clusters and estimate the ARMA coefficients in each cluster by a genetic algorithm. We also simultaneously determine the number of clusters by minimizing the Akaike information criterion (AIC). We illustrate our approach in an application to weekly product sales of a retail drugstore and focus on the specification of a genetic algorithm. First, we investigate the suitability of a k-means solution based on a distance between the ARMA coefficients as an initial solution. Second, we study the influence of the genetic algorithm parameters such as the number of generations, the size of the population, the probability of mutation, and the ratio of elite individuals.