In this paper  we introduce quantile cross-spectral analysis of multiple time series which is designed to detect general dependence structures emerging in quantiles of the joint distribution in the frequency domain . We argue that this type of dependence is natural for economic time series but remains invisible when  the traditional analysis is employed. To illustrate how such dependence structures can arise between variables in different parts of the joint distribution and across frequencies, we consider quantile vector autoregression processes. We define new estimators which capture the general dependence structure, provide a detailed analysis of their asymptotic properties and discuss how to conduct inference for a general class of possibly nonlinear processes. In an empirical illustration we examine one of the most prominent time series in economics and shed new light on the dependence of bivariate stock market returns  .
In this paper , we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains invisible when only the traditional analysis is employed. We define estimators which capture the general dependence structure, provide a detailed analysis of their asymptotic properties and discuss how to conduct inference for a general class of possibly nonlinear processes. In an empirical illustration we examine the dependence of bivariate stock market returns and shed new light on measurement of tail risk in financial markets. We also provide a modelling exercise to illustrate how applied researchers can benefit from using quantile coherency when assessing time series models .
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To illustrate how such dependence structures can arise between variables in different parts of the joint distribution and across frequencies, we consider quantile vector autoregression processes. We define new
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