Dynamic Generalized Extreme Value via Particle Filters

This thesis considers an introduction of recently developed Particle Filter algorithms and their application to Dynamic Linear models. We start from the case of a dynamic model without fixed parameter estimation to demonstrate how particle filter work. Then we show how advanced particle filters work on posterior density approximations for models that allow dynamic states and fixed parameters estimation simultaneously. It is proven that these state and parameter estimations can be achieved for these classes of dynamic models via efficient Particle Filter methods without the need of the more traditional Forward Filtering Backward Sampling (FFBS) simulation. Simulations for the first order dynamic linear model and a time-varying extreme value analysis via the Generalized Extreme Value distribution are illustrated using particle filter methods and a MCMC algorithm through sampling of full conditionals that involve a variety of Metropolis-Hastings steps. Additionally, we illustrate all the different methodologies with three practical time series of extreme values. The athletic records originally analyzed in Robinson $\\&$ Tawn (1995) and the follow-up discussions in Smith (1997) and Robinson & Tawn (1997), the maximum monthly rainfall values from January 1961 to November 1999 taken at the Maiquetia station near Caracas, Venezuela discussed in Huerta and Sanso (2007) and and Huerta and Stark (2012), the minimum daily stock returns occurring during a month from January 4, 1990 to December 28, 2007 using the Tokyo Stock Price Index (TOPIX) as in Nakajima, Kunihama, Omori and Fruhwirth-Schnatter (2011).