Quantile cointegrating regression

摘要

Quantile regression has important applications in risk management, portfolio optimization, and asset pricing. The current paper studies estimation, inference and financial applications of quantile regression with cointegrated time series. In addition,a new cointegration model with quantile-varying coefficients is proposed. In the proposed model, the value of cointegrating coefficients may be affected by the shocks and thus may vary over the innovation quantile. The proposed model may be viewed as astochastic cointegration model which includes the conventional cointegration model as a special case. It also provides a useful complement to cointegration models with (G)ARCH effects. Asymptotic properties of the proposed model and limiting distributionof the cointegrating regression quantiles are derived. In the presence of endogenous regressors, fully-modified quantile regression estimators and augmented quantile cointegrating regression are proposed to remove the second order bias and nuisance parameters. Regression Wald tests are constructed based on the fully modified quantile regression estimators. An empirical application to stock index data highlights the potential of the proposed method.