Clustering seasonal time series using extreme value analysis: An application to Spanish temperature time series

A challenging aspect of grouping together regional temperature time series is that some regions have similar summer temperatures but different winter temperatures and vice versa. We explore this by applying cluster analysis to regional temperature time series in Spain using as features the parameter estimates of location, scale, and shape, obtained from fitting the generalized extreme value (GEV) distribution to the block maxima and block minima of the series. Using this approach, our findings reveal that the identified clusters can be meaningfully interpreted and are well validated. The motivation for using this approach is that each time series is represented by just three easily extracted features. If features were to be extracted as a result of conventional time series modeling, they are likely to be impacted upon by the uncertainty of model selection. This is not the case with GEV modeling. Furthermore, GEV modeling enables long – term projections of the maxima and minima that cannot otherwise be achieved from conventional time series modeling. For comparison purposes, we also explore clustering the block maxima and block minima of the times series. In addition, we explore the performance of this approach using simulated data.