On the geometric ergodicity of nonlinear multivariate time series

2012/03/18 by Marco Ferrante, Ferrante, Marco, Giovanni Fonseca +1
Economics, Econometrics and Finance · #Financial Risk and Volatility Modeling #Complex Systems and Time Series Analysis #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1203.3984

Abstract

In this paper we consider multivariate time series obtained as solution to multidimensional nonlinear stochastic difference equations whose coefficients are allowed to be locally degenerate and to present discontinuities. We provide simple and easy to check sufficient conditions for the irreducibility, T-chain regularity and geometric ergodicity of these processes and apply the results to the BEKK-ARCH(1) models with a nonlinear autoregressive term.

Related

• On the tail behavior of a class of multivariate conditionally heteroskedastic processes
• Geometric Ergodicity of the multivariate COGARCH(1,1) Process
• Geometric ergodicity for families of homogeneous Markov chains
• On ergodic properties of nonlinear Markov chains and stochastic McKean-Vlasov equations
• The tail empirical process of regularly varying functions of geometrically ergodic Markov chains