Absolute regularity of semi-contractive GARCH-type processes

Absolute regularity and ergodicity of Poisson count processes

We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that the stationary version of the count process is absolutely regular. Moreover, since the intensities can be writte...

Misspecifying GARCH-M Processes

We consider th e relationships between ARCH-type and stochast ic volatility models. A new class of volatility models, called generalized bilinear stochastic volatility, is described following an approach that tr ansforms an init ial GARCH-M process. Th e focus here is on th e interpretation of some simulation results, with a special care devoted to model misspecification.

Regular Variation of GARCH Processes

We show that the finite-dimensional distributions of a GARCH process are regularly varying, i.e., the tails of these distributions are Pareto-like and hence heavy-tailed. Regular variation of the joint distributions provides insight into the moment properties of the process as well as the dependence structure between neighboring observations when both are large. Regular variation also plays a v...

Recursive estimation of GARCH processes

ARCH processes and their extensions known as GARCH processes are widely accepted for modelling financial time series, in particular stochastic volatility processes. The offline estimation of ARCH and GARCH processes have been analyzed under a variety of conditions in the literature. The main contribution of this paper is a rigorous convergence analysis of a recursive estimation method for GARCH...

Lecture 10: Semi-Markov Type Processes