An overview of statistical and information-theoretic aspects of hidden Markov processes
(HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain …

Abstract Models characterized by autoregressive structure and random coefficients are
powerful tools for the analysis of high-frequency, high-dimensional and volatile time series …

The LSTM network was proposed to overcome the difficulty in learning long-term
dependence, and has made significant advancements in applications. With its success and …

Provides a comprehensive and updated study of GARCH models and their applications in
finance, covering new developments in the discipline This book provides a comprehensive …

Markov Chains and Stochastic Stability is part of the Communications and Control
Engineering Series (CCES) edited by Professors BW Dickinson, ED Sontag, M. Thoma, A …

Dariusz Buraczewski Ewa Damek Thomas Mikosch The Equation X = AX + B Page 1
Springer Series in Operations Research and Financial Engineering Dariusz Buraczewski …

This classic textbook covers all aspects of risk theory in a practical way. It builds on from the
late RE Beard's extremely popular book Risk Theory, but features more emphasis on …

In this paper we consider the multivariate equation $ X_ {n+ 1}= A_ {n+ 1} X_n+ B_ {n+ 1} $
with iid coefficients which have only a logarithmic moment. We give a necessary and …

We show that the finite-dimensional distributions of a GARCH process are regularly varying,
ie, the tails of these distributions are Pareto-like and hence heavy-tailed. Regular variation of …

It is shown how Markov chain theory can be exploited to study non-linear time series, the
emphasis being on the classification into stationary and non-stationary models. A …