Clustering Discrete Valued Time Series

Abstract

There is a need for the development of models that are able to account for discreteness in data, along with its time series properties and correlation. A review of the application of thinning operators to adapt the ARMA recursion to the integer-valued case is first discussed. A class of integer-valued ARMA (INARMA) models arises from this application. Our focus falls on INteger-valued AutoRegressive (INAR) type models. The INAR type models can be used in conjunction with existing model-based clustering techniques to cluster discrete valued time series data. This approach is then illustrated with the addition of autocorrelations. With the use of a finite mixture model, several existing techniques such as the selection of the number of clusters, estimation using expectation-maximization and model selection are applicable. The proposed model is then demonstrated on real data to illustrate its clustering applications.