BAYESIAN CLASSIFICATION OF ARMA SOURCES WITH UNKNOWN ORDER

Abstract

Time series classification is a very rich subject and may be found in many areas such as economics, business, chemistry, engineering, and environmental data. This paper proposes an approximate Bayesian scheme to assign a univariate time series realization into one of several autoregressive moving average sources, with unknown coefficients and precision, that share a common unknown order. Using either a normal gamma density or a Jeffreys' prior and an approximate conditional likelihood function, the proposed assignment technique is to develop the marginal posterior mass function of a classification vector assuming the maximum of the unknown order is known. A time series realization is assigned to the r-th autoregressive moving average source whenever the classification vector has its largest value at the r-th mass point. A simulation study is carried out in order to examine the behavior and adequacy of the proposed technique with moderate realization sizes. The selected sources are chosen in such a way to include different parameters. The numerical results show that the proposed technique is practical, easy to program, and efficient in handling the classification problem of autoregressive moving average sources with unknown order.