Exponential control of the trajectories of iterated function systems with application to semi-strong GARCH models

Pub Date : 2023-05-15 DOI:10.1017/jpr.2023.13
Baye Matar Kandji
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Abstract

We establish new results on the strictly stationary solution to an iterated function system. When the driving sequence is stationary and ergodic, though not independent, the strictly stationary solution may admit no moment but we show an exponential control of the trajectories. We exploit these results to prove, under mild conditions, the consistency of the quasi-maximum likelihood estimator of GARCH(p,q) models with non-independent innovations.
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迭代函数系统轨迹的指数控制及其在半强GARCH模型中的应用
建立了一类迭代函数系统的严格平稳解的新结果。当驱动序列平稳且遍历时,虽然不是独立的,但严格平稳解可能不存在力矩,但我们展示了轨迹的指数控制。我们利用这些结果证明了在温和条件下,具有非独立创新的GARCH(p,q)模型的拟极大似然估计的相合性。
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