Propriétés de mélange des processus autorégressifs polynomiaux. (Mixing properties of polynomial autoregressive processes). (French) Zbl 0706.60040

Mokkadem, Abdelkader

Ann. Inst. Henri Poincaré, Probab. Stat. 26, No. 2, 219-260 (1990).

The mixing and the ergodicity of a Markov-chain \((Z_ n)\) is studied. A continuity theorem for the image of a measure by a polynomial application is proved. Using this result, simple sufficient conditions for the chain \((Z_ n)\) to be Harris recurrent, geometrically ergodic and geometrically absolutely regular are obtained. The last part contains applications of the results to the ARMA processes and the bilinear processes.

Reviewer: I.Valusescu

MSC:

60G10	Stationary stochastic processes
60J27	Continuous-time Markov processes on discrete state spaces
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G99	Stochastic processes

Keywords:

mixing properties; polynomial autoregressive processes; continuity theorem; image of a measure; Harris recurrent; geometrically ergodic; geometrically absolutely regular; ARMA processes; bilinear processes