Nonparametric dependence modelling for space-time cluster detection

Abstract

The dependence structures have been exhaustively studied in many applications. In this thesis, a new methodology for cluster detection is presented, i.e. the Weighted Voronoi Distance (WVD), taking into consideration not only the location of the points but also their time structure. Using variables space instead of geographical location as in spatial statistics and the torus instead of a regular Cartesian plane, this methodology allows the user to apply the rationale for more alternative scenarios. Particularly in financial markets, different dependence modelling among assets can lead to significant changes in asset allocation and different risk exposures. Besides, these dependence relationships can be used as mechanisms to detect financial crisis more quickly than fundamental models through the contagion effect. Initially, this application is run using assets from the same market, i.e. the US market, comparing the proposed methodology with methodologies mentioned in literature such as linear coefficients and copulas. This approach will be extended to assets from distinct markets in order to analyse the financial crisis dissemination across different markets. Results obtained from simulations and real data applications showed improvements compared to classical approaches especially in during turbulent financial periods.