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...

This article investigates the estimation and inference of quantile impulse response functions. We propose a new estimation method using the local projections by Jordà (2005). We establish consistency and asymptotic normality of the estimator, thereby enabling asymptotic inference. We also...

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...

This paper considers the cross-quantilogram, which measures the quantile dependence between 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...