NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS

By S. Ling, Michael Mcaleer. Econometric Theory, 2002

303 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/2333d41b65a2d9f140bc7518e790aa72809eed64

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

On linear processes with dependent innovations (2005, background): “the usual Kronecker product; let jY j be the Euclidean length of the vector Y. Assume Eð� 4 t Þo1: Ling (1999) shows that if r½EðM � 2 t Þ� o1; then fatg has a stationary distribution and Eða 4 t Þo1: Ling and McAleer [ 35 ] argue that the condition r½EðM � 2 t Þ� o1 is also necessary for the finite”
Model Averaging and Value-at-Risk Based Evaluation of Large Multi Asset Volatility Models for Risk Management (2004, unknown): “The asymptotic properties of the Gaussian PMLE have been established for certain classes of multivariate GARCH-type volatility models (see Ling and McAleer (2001) ) and it is reasonable to expect that results such as (4) and (5) would hold for the more general class of models considered in this pap”
Bartlett's formula for a general class of nonlinear processes (2009, background): “From Ling and McAleer (2002), there exists a solution to (4.”
Extreme Value Theory for GARCH Processes (2009, methodology): “a simple moment calculation involving Minkowski’s inequality and representation (3) for Yt = ae2 t imply that E(jXj2•) = E(jZj2•)E(ae2•) 29 ].”
On Adaptive Estimation in Nonstationary Arma Models with Garch Errors (2003, methodology): “Assumptions 3.2 and 3.3 are the necessary and sufficient conditions, respectively, for the finite second- and fourth-order moments of model (3.2) [see Ling (1999) and Ling and McAleer (2002)].”
The Ten Commandments for Optimizing Value-at-Risk and Daily Capital Charges (2009, unknown): “17 data, is latent (see Li, Ling and McAleer (2002) and Bauwens, Laurent and Rombouts (2006) for recent reviews). The ease of computation, even for some multivariate models, as well as its availability in several widely used econometric software packages, has made this class of models very popular. ”
An econometric analysis of asymmetric volatility : Theory and application to patents (2007, methodology): “Ling and McAleer (2002b) derived the unique strictly stationary and ergodic solution of a family of GARCH processes, which includes GJR(1,1) as a special case, a simple sufficient condition for the existence of the solution, and the necessary and sufficient condition for the existence of the…”
GARCH models without positivity constraints: Exponential or log GARCH? (2012, unknown): “Note that the conditions ρ(A(m)) 1 and ρ(C(m)) 1 are similar to those obtained by Ling and McAleer (2002) for the existence of moments of standard GARCH models.”
GARCH Models (2010, unknown): “The necessary and sufficient condition for the existence of even-order moments was established by Ling and McAleer (2002a), the sufficient part having been obtained by Chen and An (1998).”
A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries (2008, background): “Ding, Granger, and Engle (1993) discussed the Asymmetric Power ARCH model, which nests several GARCH specifications (see Ling and McAleer (2002) for a derivation of the necessary and sufficient moment conditions).”
Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)-Processes (2009, methodology): “Originally, Ling and McAleer (2002) formulated their result in terms of the spectral radius of a matrix corresponding to another state space representation of GARCH processes than the At-matrix defined in (13).”
Asymptotic theory for stationary processes (2011, background): “Ling and McAleer (2002) argue that the condition ρ[E(M⊗2t )] 1 is also necessary for the finiteness of the fourth moment.”