## Electronic Journal of Probability

### Geometric ergodicity of asymmetric volatility models with stochastic parameters

#### Abstract

In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markov-switching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existence of moments have also been investigated. Geometric ergodicity of various volatility models with stochastic parameters has been discussed as special cases.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 90, 12 pp.

Dates
Accepted: 21 October 2013
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465064315

Digital Object Identifier
doi:10.1214/EJP.v18-1871

Mathematical Reviews number (MathSciNet)
MR3126573

Zentralblatt MATH identifier
1291.60145

Rights

#### Citation

Rohan, Neelabh; Ramanathan, T. V. Geometric ergodicity of asymmetric volatility models with stochastic parameters. Electron. J. Probab. 18 (2013), paper no. 90, 12 pp. doi:10.1214/EJP.v18-1871. https://projecteuclid.org/euclid.ejp/1465064315

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