Multivariate Ecogarch Processes

First Jump Approximation of a Lévy Driven SDE and an Application to Multivariate ECOGARCH Processes

The first jump approximation of a pure jump Lévy process, which converges to the Lévy process in the Skorokhod topology in probability, is generalised to a multivariate setting and an infinite time horizon. It is shown that it can generally be used to obtain “first jump approximations” of Lévy-driven stochastic differential equations, by establishing that it has uniformly controlled variations....

Periodically correlated and multivariate symmetric stable‎ ‎processes related to periodic and cyclic flows

‎In this work we introduce and study discrete time periodically correlated stable‎ ‎processes and multivariate stationary stable processes related to periodic and cyclic‎ ‎flows‎. ‎Our study involves producing a spectral representation and a‎ ‎spectral identification for such processes‎. ‎We show that the third‎ ‎component of a periodically correlated stable process has a component related to a...

Quasi maximum likelihood estimation and prediction in the compound Poisson ECOGARCH(1,1) model

This paper deals with the problem of estimation and prediction in a compound Poisson ECOGARCH(1, 1) model. For this we construct a quasi maximum likelihood estimator under the assumption that all jumps of the log-price process are observable. Since these jumps occur at unequally spaced time points, it is clear that the estimator has to be computed for irregularly spaced data. Assuming normally ...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...