Conditional Independence Specification Testing for Dependent Processes with Local Polynomial Quantile Regression

• Main Authors: SU, Liangjun, WHITE, Halbert L.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2012
• Subjects: Conditional independence; Empirical process; Granger causality; Local polynomial; Quantile regression; Specification test; Uniform local Bahadur representation; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1433; https://ink.library.smu.edu.sg/context/soe_research/article/2432/viewcontent/hw_11_12_11_qr_ci_test.pdf
• Institution: Singapore Management University

We provide straightforward new nonparametric methods for testing conditional independence using local polynomial quantile regression, allowing weakly dependent data. Inspired by Hausman's (1978) specification testing ideas, our methods essentially compare two collections of estimators that converge to the same limits under correct specification (conditional independence) and that diverge under the alternative. To establish the properties of our estimators, we generalize the existing nonparametric quantile literature not only by allowing for dependent heterogeneous data but also by establishing a weak consistency rate for the local Bahadur representation that is uniform in both the conditioning variables and the quantile index. We also show that, despite our nonparametric approach, our tests can detect local alternatives to conditional independence that decay to zero at the parametric rate. Our approach gives the first nonparametric tests for time-series conditional independence that can detect local alternatives at the parametric rate. Monte Carlo simulations suggest that our tests perform well in finite samples. Our tests have a variety of uses in applications, such as testing conditional exogeneity or Granger non-causality.