The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series

57 Pages Posted: 11 Oct 2013 Last revised: 16 Jan 2014

See all articles by Heejoon Han

Heejoon Han

Kyung-Hee University - Department of Economics

Oliver B. Linton

University of Cambridge

Tatsushi Oka

Monash University - Department of Econometrics and Business Statistics

Yoon-Jae Whang

Seoul National University - School of Economics

Date Written: January 2014

Abstract

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 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 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.

Keywords: Quantile, Correlogram, Dependence, Predictability, Systemic risk

JEL Classification: C12, C13, C14, C22

Suggested Citation

Han, Heejoon and Linton, Oliver B. and Oka, Tatsushi and Whang, Yoon-Jae, The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series (January 2014). Available at SSRN: https://ssrn.com/abstract=2338468 or http://dx.doi.org/10.2139/ssrn.2338468

Heejoon Han (Contact Author)

Kyung-Hee University - Department of Economics ( email )

Seoul 130-701
Korea

Oliver B. Linton

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Tatsushi Oka

Monash University - Department of Econometrics and Business Statistics ( email )

Caulfield Campus
Sir John Monash Drive
Caulfield East, Victoria 3084
Australia

HOME PAGE: http://sites.google.com/site/homepageoka/

Yoon-Jae Whang

Seoul National University - School of Economics ( email )

San 56-1, Silim-dong, Kwanak-ku
Seoul 151-742
Korea
+82 2 80 6362 (Phone)
+82 2 86 4231 (Fax)

HOME PAGE: http://plaza.snu.ac.kr/~whang

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