Han, H., Linton, O., Oka, T. and Whang, Y.-J.
The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series
CWPE1452
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 the stationary bootstrap procedure; we show the consistency of this
bootstrap. Also, we consider the self-normalized approach, which is shown to be asymptotically pivotal
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, Goldman Sachs and AIG. This
article has supplementary materials online.
Keywords: Quantile, Correlogram, Dependence, Predictability, Systemic risk
Author links: Oliver Linton
PDF: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1452.pdf 
Open Access Link: https://doi.org/10.17863/CAM.5674
