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Iterated Function Systems driven by non independent sequences: structure and inference

Author

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  • Baye Matar Kandji

    (1CREST, ENSAE, Institut Polytechnique de Paris)

Abstract

The paper investigates the existence of a strictly stationary solution to an Iterated Function System (IFS) driven by a stationary and ergodic sequence. When the driving sequence is not independent, the strictly stationary solution may admit no moment but we show an exponen- tial control of the trajectories. We exploit these results to prove, under mild conditions, the consistency of the quasi-maximum likelihood es- timator of GARCH models with non independent innovations.

Suggested Citation

  • Baye Matar Kandji, 2022. "Iterated Function Systems driven by non independent sequences: structure and inference," Working Papers 2022-03, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2022-03
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    File URL: http://crest.science/RePEc/wpstorage/2022-03.pdf
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    Cited by:

    1. Baye Matar Kandji, 2023. "On the growth rate of superadditive processes and the stability of functional GARCH models," Working Papers 2023-07, Center for Research in Economics and Statistics.
    2. Christian Francq & Baye Matar Kandji & Jean-Michel Zakoian, 2022. "Inference on Multiplicative Component GARCH without any Small-Order Moment," Working Papers 2022-09, Center for Research in Economics and Statistics.

    More about this item

    Keywords

    Stochastic Recurrence Equation; Semi-strong GARCH; Quasi Maximum Likelihood; inference without moments;
    All these keywords.

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