Conditions for third-order stationarity and ergodicity of a harmonic random process

When are increment - stationary random point sets stationary ? Antoine

In a recent work, Blanc, Le Bris, and Lions defined a notion of increment-stationarity for random point sets, which allowed them to prove the existence of a thermodynamic limit for two-body potential energies on such point sets (under the additional assumption of ergodicity), and to introduce a variant of stochastic homogenization for increment-stationary coefficients. Whereas stationary random...

Random Fields: Stationarity, Ergodicity, and Spectral Behavior

Establishing Stationarity of Time Series Models via Drift Criteria

Time series models are often constructed by combining nonstationary effects such as trends with stochastic processes that are known (or believed) to be stationary. However, there are numerous time series models for which the stationarity of the underlying process is conjectured but not yet proven. We give an approachable introduction to the use of drift criteria (also known as Lyapunov function...

On Markov-switching ARMA processes – stationarity, existence of moments and geometric ergodicity

The probabilistic properties of R-valued Markov-Switching ARMA processes with a general state space parameter chain are analysed. Stationarity and ergodicity conditions are given and a feasible general stationarity condition based on a tailor-made norm is introduced. Moreover, it is shown that causality of all individual regimes is neither a necessary nor a sufficient criterion for strict negat...

Asymptotic theory for a factor GARCH model

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and βmixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estim...