Nové GAS modely s využitím extremálních rozdělení

This thesis presents three new models with time-varying parameters. These models integrate the framework of score-driven models and extreme value theory. The aim of this paper is not only to formally define the models, but also to show their application and suggest further possible extensions. Empirical validation on real data includes seismic, financial and hydrologic data. All three models have been found to be very suitable for the modelling of monthly maxima. Other suggested applications include volcanic activity, El Niño, wildfires, tsunamis, hurricanes, or in financial modeling such as catastrophic losses in insurance. Furthermore, additional research is necessary to examine the statistical properties of the models and their predictive capabilities.