High-dimensional Quantile Vector Autoregression with Influencers and Communities

Quantile vector autoregression (QVAR) models offer enhanced capabilities over vector autoregression (VAR) models in analyzing asymmetric interactions within multiple time series and are widely used in many areas, including finance and economics. However, in scenarios involving high-dimensional data where the number of time series <i>N</i> exceeds the length of the time series <i>T</i>, both parameter estimation and the theoretical establishment present significant challenges. Notably, existing research has not yet explored these challenges with the framework of QVAR models. To handle this problem, we propose a novel high-dimensional QVAR model that incorporates influencers and communities, which assumes that variables within distinct communities have shared dependency structures and are influenced by the same set of variables, called influencers. We develop an estimation procedure based on the alternating minimization algorithm and the convolution-smoothed approach. The local consistency results for the estimated parameters are established in high-dimensional settings with sub-Weibull innovations. Numerical studies illustrate that the proposed model performs well in finite samples. The proposed model is applied to identify the most influential macroeconomic variables in the United States across business cycles and construct a dynamic quantile network with influencers and communities for volatility spillover effects of global stock markets.