Spatial clustering of time series using Bayesian quantile regression

A large research literature has developed methodologies for identifying clusters of units in a spatial setting. When we deal with longitudinal or temporal data, the proposed methods are mainly based on mean regression. However, the resulting classification could not be robust in presence of outliers, skewed distributions and/or heteroscedasticity. Furthermore, the researcher might be interested in classifying units according to whether certain thresholds are exceeded. We propose a model-based approach for clustering spatial units, that is based on median or, more in general, quantile regression. In this way, we want to cope better with the aforementioned issues. The spatial units are supposed to belong to a network. The model specification is hierarchical that allows a Bayesian inference based on Markov chain Monte Carlo methods. As an illustration and motivating example, we consider data on the sea surface temperature (SST) of the Mediterranean Sea. The dataset is a result of a model re-analysis that provides 251 time series of temperature in 1-degree gridded data covering the temporal window from 1982 to 2012. Specifying a quantile of interest (e.g. in ecology, is 0.9), we aim to identify areas with similar trends and cyclic patterns.