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Weak dependence for infinite ARCH-type bilinear models. (English) Zbl 1125.62100

Summary: L. Giraitis and D. Surgailis [ARCH-type bilinear models with double long memory. Stochastic Processes Appl. 100, No. 1–2, 275–300 (2002; Zbl 1057.62070)] introduced ARCH-type bilinear models for their specific long-range dependence properties. We rather consider weak-dependence properties of these models. The computation of mixing coefficients for such models does not look as an accessible objective. So, we resort to the notion of weak dependence introduced by P. Doukhan and S. Louhichi [A new weak dependence condition and applications to moment inequalities. ibid. 84, No. 2, 313–342 (1999; Zbl 0996.60020)], whose use seems more relevant here. The decay rate of the weak-dependence coefficients sequence is established under different specifications of the model coefficients. This implies various limit theorems and asymptotics for statistical procedures. We also derive bounds for the joint densities of this model in the case of regular inputs.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60F17 Functional limit theorems; invariance principles
60F05 Central limit and other weak theorems
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References:

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