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...

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

This paper examines quantile dependence and directional predictability between the foreign exchange market and the stock market in Korea. Instead of adopting a multivariate model such as a vector autoregressive model, a multivariate GARCH model or a combination of both models, we apply 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...