In the present paper we consider the main probabilistic properties of the Markov chain Xt=aXt-1+[a0+(a1+(Xt-1)++a1-(Xt-1) -)2β]1/2εt , that we call the β-ARCH model. We examine the inevitability, irreducibility, Harris recurrence, ergodicity, geometric ergodicity, α-mixing, existence and nonexistence of finite moments and exponential moments of some order and sharp upper bounds for the tails of the stationary density of the process {Xt} in terms of the common density of the εt's.
Publié le : 1994-01-05
Classification:
autoregressive,
Markov chain,
invertibility,
ergodicity,
mixing,
tail of the stationary density,
ARCH model,
nonlinear time series,
autoregressive.,
[SHS.ECO]Humanities and Social Sciences/Economies and finances,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR],
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
@article{halshs-00199490,
author = {Diebolt, Jean and Guegan, Dominique},
title = {Probabilistic properties of the B\'eta-ARCH model},
journal = {HAL},
volume = {1994},
number = {0},
year = {1994},
language = {en},
url = {http://dml.mathdoc.fr/item/halshs-00199490}
}
Diebolt, Jean; Guegan, Dominique. Probabilistic properties of the Béta-ARCH model. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/halshs-00199490/