MIXING PROPERTIES OF A GENERAL CLASS OF GARCH(1,1) MODELS WITHOUT MOMENT ASSUMPTIONS ON THE OBSERVED PROCESS

By Christian Francq, Jean-Michel ZakoÃ¯an. Econometric Theory, 2006

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Mixing properties of ARCH and time-varying ARCH processes (2011, background): “We mention that in the case that {Xt} is a stationary, ergodic time series, [14] have shown geometric ergodicity, which they show implies β-mixing, under the weaker condition that the distribution function of {Zt} can have some discontinuities.”
Feasible invertibility conditions and maximum likelihood estimation for observation-driven models (2018, background): “Also, from the results in [23], it follows that the strong mixing assumption is always satisfied when the model is correctly specified.”
Of Copulas, Quantiles, Ranks and Spectra - An L1-Approach to Spectral Analysis (2011, background): “The class of β-mixing processes is well studied, and contains a wide range of linear and nonlinear processes, including (possibly, under mild additional assumptions) ARMA, general nonlinear scalar ARCH, threshold ARCH, and exponential ARCH processes (see Liebscher [32]), GARCH(p, q) processes with m”
ECONOMETRIC ANALYSIS OF VOLATILITY COMPONENT MODELS (2014, background): “The study on matrix product goes back to Furstenberg and Kesten (1960), Furstenberg (1963) (See Goldsheid (1991) for a comprehensive review). Kesten and Spitzer (1984) studied the convergence of product of iid nonnegative matrices.”
Merits and Drawbacks of Variance Targeting in GARCH Models (2011, background): “Carrasco, M. and X. Chen (2002) Mixing and moment properties of various GARCH and stochastic volatility models.”