Inference and testing on the boundary in extended constant conditional correlation GARCH models

Abstract

We consider inference and testing in extended constant conditional correlation GARCH models in the case where the true parameter vector is a boundary point of the parameter space. This is of particular importance when testing for volatility spillovers in the model. The large-sample properties of the QMLE are derived together with the limiting distributions of the related LR, Wald, and LM statistics. Due to the boundary problem, these large-sample properties become nonstandard. The size and power properties of the tests are investigated in a simulation study. As an empirical illustration we test for (no) volatility spillovers between foreign exchange rates.

Dynamic Conditional Eigenvalue GARCH

“…In line with Pedersen and Rahbek (2019), one may need stronger moment conditions than the ones in Assumption 3.7 in order to prove tightness. Likewise, due to the fact that 0 is a boundary point of , it may require higher-order moments of X t in order so show that ratios of the type (16) have …nite expectation, similar to Francq and Zakoïan 2009and Pedersen (2017) where …nite sixth-order moments are imposed.…”

“…A relevant hypothesis to test is if there are no spillovers between the eigenvalues, that is if the matrices A and B are diagonal, similar to testing for no volatility spillovers in ECCC-GARCH models as considered by Pedersen (2017). We here take another direction and consider testing of the hypothesis that one or more linear combinations of t are constant.…”

The long memory HEAVY process: modeling and forecasting financial volatility

“…Moreover, Pedersen and Rahbek (2019) developed likelihood-ratio tests on the significance of the nonstationary covariate in the above mentioned model, while Halunga and Orme (2009) provided some asymmetry and nonlinearity tests. Lastly, Nakatani and Teräsvirta (2009) and Pedersen (2017) focused on the multivariate case, the so called extended constant conditional correlation, which allows for volatility spillovers and they developed inference and testing for the quasimaximum likelihood estimator (QMLE) parameters (see also Ling and McAleer 2003 for the asymptotic theory of vector ARMA-GARCH processes). Within the HEAVY framework we first estimate the benchmark formulation as in Shephard and Sheppard (2010), that is, without asymmetries and power transformations, obtaining very similar results (available upon request).…”

Asymptotics of Cholesky GARCH models and time-varying conditional betas

“…An attractive feature of the Cholesky-GARCH (CHAR) model is that the dynamics of ϵ t can be defined by specifying successively the dynamics of the vector v t of the orthogonal factors and the dynamics of the vector ℓ t = vech 0 L t of the subdiagonal elements of L t , or alternatively the dynamics of β t = −vech 0 B t . 3 We illustrate our general framework by first considering, for the dynamics of this specification, the Extended Constant Conditional correlation GARCH model studied by Jeantheau (1998), Ling and McAleer (2003), He and Teräsvirta (2004), Aue et al (2009), Francq and Zakoïan (2010) and Pedersen (2017), among others. This model assumes that…”