Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)-Processes

By A. Lindner. 2009

112 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c34cdec864a5733bc3ed14b002126d99b77b0143

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Citations in the corpus

ECONOMETRIC ANALYSIS OF VOLATILITY COMPONENT MODELS (2014, background): “…assumption that εt is absolutely continuous with strictly positive Lebesgue density in a neighborhood of zero, Yt is geometrically ergodic and hence rt is β-mixing, which follows from Mokkadem (1990) (or Theorem 1 of Carrasco and Chen, 2002; Theorem 8 of Lindner, 2009). n Proof of Proposition 3.3.”
Inference in VARs with Conditional Heteroskedasticity of Unknown Form (2016, methodology): “Hence, one can focus on verifying whether the 8-th moment of a GARCH process exists for given GARCH parameters and the conditional distribution, compare Ling & McAleer (2002), Lindner (2009).”
Extreme Value Theory for GARCH Processes (2009, methodology): “a simple moment calculation involving Minkowski’s inequality and representation (3) for Yt = σ 2 t imply that E(|X| 2κ )= E(|Z| 2κ ) E(σ 2κ ) Lindner (2008) .”
Stationarity and geometric ergodicity of BEKK multivariate GARCH models (2011, background): “In the univariate case it is well-known that for a driving noise ε with finite variance one may well choose the GARCH parameters in such a way that a unique stationary solution with infinite second moments exists (see [2, 7, 24], for example).”
Mixing properties of ARCH and time-varying ARCH processes (2011, methodology): “i,j |P (Gi ∩Hj) − P (Gi)P (Hj)|, where r1, r2 ≥ 0 and {Gi} and {Hi} are partitions of Ω. In the proposition below, we give a bound for the mixing rate in terms of conditional densities. Similar bounds for linear processes have been derived in Chanda (1974) and Gorodetskii (1977) (see also Davidson (”
Probabilistic Properties of Stochastic Volatility Models (2009, methodology): “2 Conditions for the existence of a stationary GARCH process are much more difficult to establish, see Nelson (1990) and Bougerol and Picard (1992), cf. Lindner (2008) .”