Bayesian Fuzzy Clustering with Robust Weighted Distance for Multiple ARIMA and Multivariate Time-Series

The paper suggests and develops a computational approach to improve hierarchical fuzzy clustering time-series analysis when accounting for high dimensional and noise problems in dynamic data. A Robust Weighted Distance measure between pairs of sets of Auto-Regressive Integrated Moving Average models is used. It is robust because Bayesian Model Selection methodology is performed with a set of conjugate informative priors in order to discover the most probable set of clusters capturing different dynamics and interconnections among time-varying data, and weighted because each time-series is 'adjusted' by own Posterior Model Size distribution in order to group dynamic data objects into 'ad hoc' homogenous clusters. Monte Carlo methods are used to compute exact posterior probabilities for each cluster chosen and thus avoid the problem of increasing the overall probability of errors that plagues classical statistical methods based on significance tests. Empirical and simulated examples describe the functioning and the performance of the procedure. Discussions with related works and possible extensions of the methodology to jointly deal with endogeneity issues and misspecified dynamics in high dimensional multicountry setups are also displayed.