The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series
The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series
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DOI：
10.2139/ssrn.2338468
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发表时间：
2014-01
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影响因子：
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通讯作者：
Heejoon Han;O. Linton;Tatsushi Oka;Yoon-Jae Whang
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文献类型：
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作者：
Heejoon Han;O. Linton;Tatsushi Oka;Yoon-Jae Whang
本文提出了交叉分位数图来衡量两个时间序列之间的分位数依赖性。我们应用它来检验一个时间序列对另一个时间序列没有方向可预测性的假设。我们建立了交叉量化图的渐近分布和相应的检验统计量。限制分布取决于干扰参数。为了构建一致的置信区间，我们采用固定引导程序；我们建立了这个引导程序的一致性。此外，我们还考虑了一种自归一化方法，该方法在不可预测性的零假设下产生渐近关键统计量。我们提供模拟研究和两个实证应用。首先，我们使用交叉量化图来检测从股票方差到超额股票回报的可预测性。与股票收益可预测性文献中使用的现有工具相比，我们的方法提供了预测变量和股票收益之间更完整的关系。其次，我们调查个别金融机构的系统性风险，例如摩根大通、摩根士丹利和AIG。
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.