Time series clustering using trend, seasonal and autoregressive components to identify maximum temperature patterns in the Iberian Peninsula

Abstract

Time series (TS) clustering is a crucial area of data mining that can be used to identify interesting patterns. This study introduces a novel approach to obtain clusters of TS by representing them with feature vectors that define the trend, seasonality and noise components of each series in order to identify areas of the Iberian Peninsula (IP) that follow the same pattern of change in regards to maximum temperature during 1931–2009. This representation allows for dimensionality reduction, and is obtained based on singular spectrum analysis decomposition in a sequential manner, which is a well-developed methodology of TS analysis and forecasting with applications ranging from the decomposition and filtering of nonparametric TS to parameter estimation and forecasting. In this approach, the trend, seasonality and residual components of each TS corresponding to a specific area in the Iberian region are extracted using the proposed SSA methodology. Afterwards, the feature vectors of the TS are obtained by modelling the extracted components and estimating their parameters. Finally, a clustering algorithm is applied to group the TS into clusters, which are defined according to the centroids. This methodology is applied to a climate database with reasonable results that align with the defined characteristics, enabling a spatial exploration of the IP. The results identified three differentiated zones that can be used to describe how the maximum temperature varied: in the northern and central zones, an increase in temperature was noted over time, whereas in the southern zone, a slight decrease was noted. Moreover, different seasonal variations were observed across the zones.