Stationarity and geometric ergodicity of a class of nonlinear ARCH models

DOI10.1214/105051606000000565zbMath1121.60033arXivmath/0702419OpenAlexW2043773425MaRDI QIDQ997428

Youssef Saïdi, Jean-Michel Zakoian

Publication date: 6 August 2007

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702419

zbMATH Keywords

Markov chains\(\beta\)-mixingergodicitynonlinear time seriesthreshold modelsGARCH-type models

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Stationary stochastic processes (60G10) Economic time series analysis (91B84) Discrete-time Markov processes on general state spaces (60J05)

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Cites Work

• Unnamed Item
• Markov chains and stochastic stability
• Fractionally integrated generalized autoregressive conditional heteroskedasticity
• Stationarity of GARCH processes and of some nonnegative time series
• Strict stationarity of generalized autoregressive processes
• Verifying irreducibility and continuity of a nonlinear time series
• Regular variation of GARCH processes.
• Stability and the Lyapounov exponent of threshold AR-ARCH models
• Stationarity and the existence of moments of a family of GARCH processes.
• Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure.
• Non-linear time series and Markov chains
• Conditional Heteroskedasticity in Asset Returns: A New Approach
• A threshold AR(1) model
• MIXING PROPERTIES OF A GENERAL CLASS OF GARCH(1,1) MODELS WITHOUT MOMENT ASSUMPTIONS ON THE OBSERVED PROCESS
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• Mixing Conditions for Markov Chains
• MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS
• Threshold heteroskedastic models