A Projection-Based Nonparametric Test of Conditional Quantile Independence

This paper proposes a nonparametric procedure for testing conditional quantile independence using projections. Relative to existing smoothed nonparametric tests, the resulting test statistic: (i) detects the high frequency local alternatives that converge to the null hypothesis in probability at faster rate and, (ii) yields improvements in the finite sample power when a large number of variables are included under the alternative. In addition, it allows the researcher to include qualitative information and, if desired, direct the test against specific subsets of alternatives without imposing any functional form on them. We use the weighted Nadaraya-Watson (WNW) estimator of the conditional quantile function avoiding the boundary problems in estimation and testing and prove weak uniform consistency (with rate) of the WNW estimator for absolutely regular processes. The procedure is applied to a study of risk spillovers among the banks. We show that the methodology generalizes some of the recently proposed measures of systemic risk and we use the quantile framework to assess the intensity of risk spillovers among individual financial institutions.