Fourth Moment Structure of Multivariate GARCH Models

By Christian M. Hafner. 2003

76 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/7cc5a2d07962304ace3b8f08b5cabbe34b40b8f4

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Citations in the corpus

Temporal aggregation of multivariate GARCH processes (2004, methodology): “Theorem 4 Under Assumptions 1 to 3, the asymptotic distribution of realized volatilities for m →∞ is given by m−1/2(η̄mt −mσ) D−→ N (0, 2πf(0)) where f(λ) is the spectral density matrix of ηt at frequency λ given in (46).”
GARCH Models (2010, unknown): “Hafner (2003) and He and Teräsvirta (2004) studied the fourth-order moments of multivariate GARCH models.”
Inference in VARs with Conditional Heteroskedasticity of Unknown Form (2016, methodology): “Gonçalves & Kilian (2004, 2007) and Hafner & Herwartz (2009). Second, we analyze the theoretical properties of different bootstrap approaches commonly used in a VAR context with conditional heteroskedasticity. Our result here indicates that neither a wild bootstrap (recursive-design and fixed-design”
The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility (2010, unknown): “If the order of the CAW(p, q) model is small, it is possible to obtain a more convenient expression for the second moment than that in Equation (17).”
Necessary and Sufficient Restrictions for Existence of a Unique Fourth Moment of a Univariate Garch(P,Q) Process (2005, background): “Various papers in the literature claim to prove necessity and sufficiency of restrictions for 4th-moment existence in univariate GARCH processes, but most do not discuss any sort of nonnegativity (e.g., Hafner, 2003).”
Multivariate GARCH models (2008, unknown): “The fourth-moment structure of the BEKK and VEC models is investigated by Hafner (2003), who gives necessary and sufficient conditions for the existence of the fourth moments and provides expressions for them.”
Stationarity and geometric ergodicity of BEKK multivariate GARCH models (2011, methodology): “Moreover, combining our conditions on geometric ergodicity with the four th order moment conditions of [18] immediately gives sufficient conditions for the validity of more classical CLTs.”
Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity (2009, methodology): “In the special case of a stationary multivariate GARCH process investigated in section 3, W = E[(Zt−1Z ′t−1) ⊗ (utu′t)], which could be calculated analytically by extending results of Hafner (2003) to the VAR-GARCH case.”
Multivariate GARCH Models: A Survey (2003, unknown): “Hafner (2003) provides analytical expressions of the fourth order moments of the general VEC model.”
Multivariate High-Frequency-Based Volatility (HEAVY) Models (2012, background): “…for assets 1 and 2, respectively, and hij, i, j D 1, 2, are the elements of Ht. Applying a vec operator to (A.3) gives a similar result to (10) in Hafner (2003), which discusses the fourth moment structure of GARCH models when Ht follows a GARCH specification and daily returns are assumed to be…”
Volatility impulse responses for multivariate GARCH models: An exchange rate illustration (2006, background): “For the multinormal and multivariate t distribution cases, an explicit expression for Sh can be found in Hafner (2003). If the baseline is set to zero, then Z31⁄4 0 and the variance of vt reduces to FtShFt.”
MGARCH models: Trade-off between feasibility and flexibility (2018, background): “Furthermore, Hafner (2003) derives analytical expressions of the fourth order moments of returns and Hafner and Preminger (2009) establish sufficient conditions for geometric ergodicity.”
Temporal aggregation of univariate and multivariate time series models: a survey (2008, unknown): “31), we need all the eigenvalues of the matrix Z = ((A ⊗A)G2 + A ⊗B + B ⊗A + B ⊗B) (34) to have modulus smaller than one for the fourth moments to be finite.”
ASYMPTOTIC THEORY FOR A FACTOR GARCH MODEL (2009, unknown): “Based on the vector autoregressive moving average (VARMA) representation we can show similar to Hafner (2003) that the fourth moments of ft and the τ -autocorrelation of ηt , (τ) = E[(ηt −σ 2)(ηt−τ −σ 2)], are given by E[vec( η)] = Mξ (IN 2 − Z)−1vec{ιι′ + (A + B)σ 2ι′ + ισ 2 ′ (A + B)′} and (τ) =…”