MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS

By M. Carrasco, Xiaohong Chen. 2002

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Subfields: Finance, Statistics and Probability

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Citations in the corpus

Smoothed Dual Embedding Control (2017, background): “ 1 ensures the solvability of the MDP and boundedness of the optimal value functions, V and V~ . Assumption 2 ensures -mixing property of the samples f(s i;a i;R i)g t i=1 (see e.g., Proposition 4 in Carrasco and Chen (2002)) and is often necessary to prove large deviation bounds. The error introduc”
Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates (2013, unknown): “Carrasco and Chen (2002). Since wt and xt are independent and f (x) = 1/ ( ω0 + π0x 2 )2 is integrable, we can employ Lemma 6(i) to obtain −nHn,ωω(θ0)→d Hnst ωω .”
TESTING FOR A CHANGE IN CORRELATION AT AN UNKNOWN POINT IN TIME USING AN EXTENDED FUNCTIONAL DELTA METHOD (2011, background): “In particular, Assumption (A3) allows for generalized autoregressive conditional heteroskedasticity (GARCH) effects (see, e.g., Hansen, 1991; Carrasco and Chen, 2002), which are observed in financial data.”
Random Forests for dependent data (2020, methodology): “We focus on absolutely regular or β-mixing processes, as on one hand these class of stochastic processes are rich enough to accommodate many commonly used dependent error structures like ARMA [49], GARCH [11], certain Markov processes [22], Gaussian process with Matérn covariance family.”
A Double AR(p) Model: Structure and Estimation (2007, unknown): “This method has been commonly used to find sufficient conditions for stationarity of nonlinear time series models, see for example Tong (1990), Chen and An (1998, 1999), Carrasco and Chen (2002) and Ling and McAleer (2002).”
Mixing properties of ARCH and time-varying ARCH processes (2011, background): “Related results on mixing for GARCH(p, q) processes can be found in [8, 25, 26, 35] (for an excellent review) and [14, 27] (where mixing of ‘nonlinear’ GARCH(p, q) processes is also considered).”
Realized GARCH: a joint model for returns and realized measures of volatility (2012, unknown): “…stationary and β -mixing with exponential decay, and { ( r t , x t ) , t ≥ 0 } is a generalized hidden Markov model, with hidden chain { ˜ h t , t ≥ 0 } , and so by Carrasco and Chen (2002, proposition 4) it follows that also { ( r t , x t ) } is stationary β -mixing with exponentially decay rate.”
Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data (2015, background): “Carrasco and Chen (2002) provide the conditions that make GARCH processes stationary and β-mixing with exponential decay, whereas Chen, Hansen, and Carrasco (2010) discuss the conditions that can establish β-mixing with exponential decay in scalar diffusion processes.”
Copula-Based Models for Financial Time Series (2009, background): “In situations where the researcher has accumulated knowledge about the distributions of the individual variables and wants to use that in constructing a joint distribution, copulas also have a valuable role.”
Nonparametric Inference of Value-at-Risk for Dependent Financial Returns (2005, background): “Carrasco and Chen (2002) provides general conditions that ensure the above GARCH (p, q) model as a special case of the generalized hidden Markov models is geometric b-mixing [see Doukhan (1994) 230 Journal of Financial Econometrics”
Nonparametric Estimation of Expected Shortfall (2007, methodology): “For instance Carrasco and Chen (2002) established the α-mixing for ARCH model; and Genon–Catalot, Jeantheau, and Larédo (2000) for diffusion models.”
Dynamic Orthogonal Components for Multivariate Time Series (2011, methodology): “(14) Applying the theorems of He et al. (1999) and Carrasco and Chen (2002), we note that these are sufficient conditions for strict stationarity and strong mixing with a geometric rate for the GARCH(1,1)-t model, and necessary and sufficient conditions to ensure Assumption 2 for the Huber2.”