The detection of patterns in multivariate time series with ¿contiguity¿ constraints is a relevant task, especially for large datasets. The research aims at proposing clustering models for multivariate time series, with the following characteristics.
First, the Partitioning Around Medoids (PAM) framework is considered.
Among the different approaches to the clustering of multivariate time series, the observation-based is adopted.
To cope with the complexity of the features of each multivariate time series and the associated assignment uncertainty a fuzzy clustering approach is adopted.
To neutralize the effect of possible outliers, the noise, metric and trimmed approach are considered.
The temporal aspect will be dealt with by using appropriate measures of dissimilarity between time trajectories; the contiguity among units by adding a contiguity matrix as a penalization term in the clustering model.
In socio-economic clustering often the empirical information is represented by time-varying data generated by indicators observed over time on a set of territorial units. Usually among these units may exist contiguity relations, spatial but not only. The proposed models are intended to be applied to the classification of the European NUTs on the basis of the observed dynamics of the Basic, Efficiency and Innovation subindexes of the Regional Competitiveness Index (RCI) 2013 and 2016.
The research represents an improvement in the methods of fuzzy classification with respect to the temporal aspect of the data (and related comparability over time), the presence of contiguity ¿ not necessarily spatial - constraints among the units and the robustness to outliers.
The application of the proposed models to the classification of the European NUTs on the basis of the observed dynamics of the subindexes and of the indicators of the Regional Competitiveness Index (RCI) will be considered. The Regional Competitiveness Index (RCI) (Annoni et al., 2017) is a Composite Indicator composed of 11 pillars that describe the different aspects of competitiveness. The pillars are classified into three groups (subindexes): Basic, Efficiency and Innovation.
In socio-economical clustering often the empirical information is represented by time-varying data generated by Composite Indicators (CIs) observed over time on a set of subnational (regional) units. Usually among the units may exist contiguity relations, spatial but not only. Composite indicators (CIs) which compare country performance are increasingly recognized as a useful tool in policy analysis and public communication. The number of CIs in existence around the world is growing year after year. Such composite indicators provide simple comparisons of countries that can be used to illustrate complex and sometimes elusive issues in wide-ranging fields, e.g., environment, economy, society or technological development (OECD 2016a, 2016b). A composite indicator is formed when individual indicators are compiled into a single index on the basis of an underlying model. The composite indicator should ideally measure multi-dimensional concepts which cannot be captured by a single indicator, such as competitiveness, industrialisation, sustainability, single market integration, knowledge-based society. The Composite Indicators are often undertaken by international institutions of Official Statistics (Eurostat, OECD, WEF, World Bank).
The classification and positioning of the (geographic) units with respect to the indicators is generally developed using Cluster Analysis. When time information is available, the data are three-way data of type same units, same variables, time. Two relevant questions that arise are: i) the temporal analysis of single/composite indicators and ii) the presence of some relations among units, spatial but not only.
Annoni, P., Dijkstra, L., Gargano, N., The EU Regional Competitiveness Index 2016, WP 02/2017, 28, Luxembourg Publications Office of the European Union, (2017).