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Characteristic Function Based Testing For Conditional Independence: A Nonparametric Regression Approach

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  • Wang, Xia
  • Hong, Yongmiao

Abstract

We propose a characteristic function based test for conditional independence, applicable to both cross-sectional and time series data. We also derive a class of derivative tests, which deliver model-free tests for such important hypotheses as omitted variables, Granger causality in various moments and conditional uncorrelatedness. The proposed tests have a convenient asymptotic null N (0, 1) distribution, and are asymptotically locally more powerful than a variety of related smoothed nonparametric tests in the literature. Unlike other smoothed nonparametric tests for conditional independence, we allow nonparametric estimators for both conditional joint and marginal characteristic functions to jointly determine the asymptotic distributions of the test statistics. Monte Carlo studies demonstrate excellent power of the tests against various alternatives. In an application to testing Granger causality, we document the existence of nonlinear relationships between money and output, which are missed by some existing tests.

Suggested Citation

  • Wang, Xia & Hong, Yongmiao, 2018. "Characteristic Function Based Testing For Conditional Independence: A Nonparametric Regression Approach," Econometric Theory, Cambridge University Press, vol. 34(4), pages 815-849, August.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:04:p:815-849_00
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    Cited by:

    1. Viktor Todorov & Yang Zhang, 2022. "Information gains from using short‐dated options for measuring and forecasting volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 368-391, March.
    2. Black, Dan A. & Joo, Joonhwi & LaLonde, Robert & Smith, Jeffrey A. & Taylor, Evan J., 2022. "Simple Tests for Selection: Learning More from Instrumental Variables," Labour Economics, Elsevier, vol. 79(C).
    3. Xiaojun Song & Haoyu Wei, 2021. "Nonparametric Tests of Conditional Independence for Time Series," Papers 2110.04847, arXiv.org.
    4. Shi, Chengchun & Xu, Tianlin & Bergsma, Wicher & Li, Lexin, 2021. "Double generative adversarial networks for conditional independence testing," LSE Research Online Documents on Economics 112550, London School of Economics and Political Science, LSE Library.
    5. Zhou, Yeqing & Liu, Jingyuan & Zhu, Liping, 2020. "Test for conditional independence with application to conditional screening," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    6. Ning, Jing & Pak, Daewoo & Zhu, Hong & Qin, Jing, 2022. "Conditional independence test of failure and truncation times: Essential tool for method selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    7. Xuehu Zhu & Jun Lu & Jun Zhang & Lixing Zhu, 2021. "Testing for conditional independence: A groupwise dimension reduction‐based adaptive‐to‐model approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 549-576, June.
    8. Maomao Ding & Ruosha Li & Jin Qin & Jing Ning, 2023. "A double‐robust test for high‐dimensional gene coexpression networks conditioning on clinical information," Biometrics, The International Biometric Society, vol. 79(4), pages 3227-3238, December.

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