This paper investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE?s) of the GARCH model augmented by including an additional explanatory variable - the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as...

This article investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE's) of the GARCH model augmented by including an additional explanatory variable-the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as...

This paper analyzes the effect of omitting a persistent covariate in the GARCH-X model. In particular, we show that if the relevant persistent covariate is omitted and the usual GARCH(1,1) model is fitted, the model will be estimated approximately as an IGARCH model. This may well explain the...

The KOSPI 200 options are one of the most actively traded derivatives in the world. This paper empirically examines (a) the statistical properties of the Korea's representative implied volatility index (VKOSPI) derived from the KOSPI 200 options and (b) macroeconomic and financial variables that...

This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross quantilogram and the...

We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCH-NNH model, that is an ARCH(1) process with a nonlinear function...

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of...

The paper considers a volatility model which introduces a persistent, integrated or near-integrated, covariate to the standard GARCH(1, 1) model. For such a model, we derive the asymptotic theory of the quasi-maximum likelihood estimator. In particular, we establish consistency and obtain limit...