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

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 resu...

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Bibliographic Details
Published inJournal of applied probability Vol. 60; no. 4; pp. 1501 - 1515
Main Author Kandji, Baye Matar
Format Journal Article
LanguageEnglish
Published Sheffield Cambridge University Press 01.12.2023
Subjects
Autoregressive models
Econometrics
Maximum likelihood estimators
Stochastic models
Trajectory control
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ISSN0021-9002
1475-6072
DOI10.1017/jpr.2023.13

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Summary: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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ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2023.13