English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The first motivation of this paper is to study stationarity and ergodicproperties for a general class of time series models defined conditional on anexogenous covariates process. The dynamic of these models is given by anautoregressive latent process which forms a Markov chain in randomenvironments. Contrarily to existing contributions in the field of Markovchains in random environments, the state space is not discrete and we do notuse small set type assumptions or uniform contraction conditions for the randomMarkov kernels. Our assumptions are quite general and allows to deal withmodels that are not fully contractive, such as threshold autoregressiveprocesses. Using a coupling approach, we study the existence of a limit, inWasserstein metric, for the backward iterations of the chain. We also deriveergodic properties for the corresponding skew-product Markov chain. Our resultsare illustrated with many examples of autoregressive processes widely used instatistics or in econometrics, including GARCH type processes, countautoregressions and categorical time series.

Stationarity and ergodic properties for some observation-driven models in random environments