Finite Mixture Modeling of Gaussian Regression Time Series with Application to Dendrochronology

Finite mixture modeling is a popular statistical technique capable of accounting for various shapes in data. One popular application of mixture models is model-based clustering. This paper considers the problem of clustering regression autoregressive moving average time series. Two novel estimation procedures for the considered framework are developed. The first one yields the conditional maximum likelihood estimates which can be used in cases when the length of times series is substantial. Simple analytical expressions make fast parameter estimation possible. The second method incorporates the Kalman filter and yields the exact maximum likelihood estimates. The procedure for assessing variability in obtained estimates is discussed. We also show that the Bayesian information criterion can be successfully used to choose the optimal number of mixture components and correctly assess time series orders. The performance of the developed methodology is evaluated on simulation studies. An application to the analysis of tree ring data is thoroughly considered. The results are very promising as the proposed approach overcomes the limitations of other methods developed so far.