The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series

Abstract

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 corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confidence intervals we employ a stationary bootstrap procedure; we establish consistency of this bootstrap. Also, we consider a self-normalized approach, which yields an asymptotically pivotal statistic under the null hypothesis of no predictability. We provide simulation studies and two empirical applications. First, we use the cross-quantilogram to detect predictability from stock variance to excess stock return. Compared to existing tools used in the literature of stock return predictability, our method provides a more complete relationship between a predictor and stock return. Second, we investigate the systemic risk of individual financial institutions, such as JP Morgan Chase, Morgan Stanley and AIG.

Predictive quantile regression with persistent covariates: IVX-QR approach

“…The linear dependence ( ) a¤ ects the distortion of nonstationary mean regression, while ( ) contributes to the distortion in nonstationary QR. If we consider a quantile-quantile predictability (Han et al, 2014) or a extreme quantile version of it (Davis and Mikosch, 2009), L ( ) or L will play the contributing role for the distortion. The quantile-quantile predictability under the presence of persistent predictors will be an interesting topic for future research, wherein we would need to de…ne a proper version of quantile for nonstationary processes.…”

“…These last two papers can be classi…ed as part of the predictive QR literature since they focus on the prediction of stock return quantiles from lagged …nancial variables. Another piece of related research is Han et al (2014) which studies the quantile dependence between stock return and a predictor, wherein the new analysis becomes possible by extending quantilogram theory (Linton and Whang, 2007) to the cross-quantilogram. In the mean predictive regression literature, Gonzalo and Pitarakis (2012) and Kostakis et al (2012) are close to this paper, since they have also applied the IVX methodology to the stock return regression.…”

Directional predictability from stock market sector indices to gold: A cross-quantilogram analysis

“…We address the safe haven properties of gold relative to US stock market sector indices using the bivariate cross-quantilogram of Han et al (2016). Splitting our sample into pre-and post-crisis periods, our results show that the safe haven properties of gold have a changing nature.…”

“…To analyze the position of gold as a safe haven, we use the bivariate cross-quantilogram of Han et al (2016). In a recent contribution, Han et al (2016) another.…”

“…In this paper, we contribute to the "gold as a safe haven" literature by applying the new methodology proposed by Han et al (2016), which allows us to measure the directional quantile dependence between gold and stock market returns. As noted by Liu et al (2016), the conventional approaches may not be appropriate measures of dependence between stock and gold returns when the bivariate normality assumption on the joint distribution does not hold.…”