L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term
✍ Scribed by Zudi Lu; Zhenyu Jiang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 118 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0167-7152
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✦ Synopsis
In this note, the condition to ensure the L1 geometric ergodicity of a multivariate nonlinear AR model mixed with an ARCH term (also called conditional heteroscedastic autoregressive nonlinear model) is investigated. Under some mild conditions on the white noise process with ÿrst absolute moment, a su cient condition much weaker than that by Ango Nze (C.R. Acad. Sci. Paris 315 ser. 1 (1992) 1301-1304) is derived. As an application, the L1 geometric ergodicity of an additive AR model mixed with a multiplicative ARCH term is studied. Our condition expands the application of the result in Ango Nze (C.R. Acad. Sci. Paris 315 ser. 1 (1992) 1301-1304) and is interesting for robust modeling when the white noise is fat-tailed with inÿnite variance. Some additional remarks are also made.