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On the estimation of [beta]-ARCH models

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  • Hili, Ouagnina

Abstract

The parametric [beta]-ARCH model which is defined byXt=aXt-1+(a0+a1Xt-12[beta])1/2[var epsilon]thas been introduced by Diebolt and Guégan (C. R. Acad. Sci. Paris 312(I) (1991) 33-36). The probabilistic properties of this model are well known (see Guégan and Diebolt, 1994). In this paper, we derive under mild conditions the asymptotic properties (consistency and asymptotic normality) of the minimum Hellinger distance estimates of the parameters a,a0,a1 and [beta]. The generalisation to an homogeneous Markov chain of order p>1 is also considered.

Suggested Citation

  • Hili, Ouagnina, 1999. "On the estimation of [beta]-ARCH models," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 285-293, December.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:4:p:285-293
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    References listed on IDEAS

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    1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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