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A consistent characteristic function-based test for conditional independence

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  • Su, Liangjun
  • White, Halbert

Abstract

This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We use the functional delta method to expand the test statistic around the population truth and establish asymptotic normality under $\beta -$mixing conditions. We show that the test is consistent and has power against local alternatives at distance $n^{-1/2}h_{1}^{-(d_{1}+d_{3})/4}.$ The cases for which not all random variables of interest are\ continuously valued or observable are also treated, and we show that the test is nuisance-parameter free. Simulation results suggest that the test has better finite sample performance than the Hellinger metric test of Su and White (2002) in detecting nonlinear Granger causality in the mean. Applications to exchange rates and to stock prices and trading volumes indicate that our test can reveal some interesting nonlinear causal relations that the traditional linear Granger causality test fails to detect.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 141 (2007)
Issue (Month): 2 (December)
Pages: 807-834

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Handle: RePEc:eee:econom:v:141:y:2007:i:2:p:807-834

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(04), pages 576-601, August.
  2. Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
  3. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, Elsevier, vol. 20(1), pages 105-134, October.
  4. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July.
  5. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  6. Sheedy, Elizabeth, 1998. "Correlation in currency markets a risk-adjusted perspective," Journal of International Financial Markets, Institutions and Money, Elsevier, Elsevier, vol. 8(1), pages 59-82, January.
  7. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, Elsevier, vol. 84(2), pages 205-231, June.
  8. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, Econometric Society, vol. 73(3), pages 837-901, 05.
  9. Lobato, Ignacio N, 2003. "Testing for Nonlinear Autoregression," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 21(1), pages 164-73, January.
  10. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, Elsevier, vol. 92(1), pages 101-147, September.
  11. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(01), pages 1-31, February.
  12. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  13. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
  14. Efstathios Paparoditis & Dimitris Politis, 2000. "The Local Bootstrap for Kernel Estimators under General Dependence Conditions," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(1), pages 139-159, March.
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Citations

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Cited by:
  1. Chia-Chang Chuang & Chung-Ming Kuan & Hsin-yi Lin, 2007. "Causality in Quantiles and Dynamic Stock Return-Volume Relations," IEAS Working Paper : academic research 07-A006, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  2. Bin Chen & Yongmiao Hong, 2013. "Characteristic Function-Based Testing for Multifactor Continuous-Time Markov Models via Nonparametri," Papers 2013-10-14, Working Paper.
  3. repec:wyi:journl:002117 is not listed on IDEAS
  4. Taoufik Bouezmarni & Jeroen V. K. Rombouts & Abderrahim Taamouti, 2009. "A nonparametric copula based test for conditional independence with applications to granger causality," Economics Working Papers we093419, Universidad Carlos III, Departamento de Economía.
  5. Bertrand Caudelon & Sessi Tokpavi, 2014. "A Nonparametric Test for Granger-causality in Distribution with Application to Financial Contagion," EconomiX Working Papers 2014-18, University of Paris West - Nanterre la Défense, EconomiX.
  6. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, Elsevier, vol. 164(2), pages 268-293, October.
  7. Nadarajah, Saralees & Chan, Stephen & Afuecheta, Emmanuel, 2013. "On the characteristic function for asymmetric Student t distributions," Economics Letters, Elsevier, vol. 121(2), pages 271-274.
  8. repec:wyi:journl:002142 is not listed on IDEAS
  9. Nianqing Liu & Quang Vuong & Haiqing Xu, 2012. "Rationalization and Identification of Discrete Games with Correlated Types," Department of Economics Working Papers 130915, The University of Texas at Austin, Department of Economics.
  10. Huang, Meng & Sun, Yixiao & White, Hal, 2013. "A Flexible Nonparametric Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series qt3pt89204, Department of Economics, UC San Diego.
  11. Matos, João Manuel Gonçalves Amaro de & Fernandes, Marcelo, 2001. "Testing The Markov Property with Ultra High Frequency Financial Data," Economics Working Papers (Ensaios Economicos da EPGE) 414, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  12. Amaro de Matos, Joao & Fernandes, Marcelo, 2007. "Testing the Markov property with high frequency data," Journal of Econometrics, Elsevier, Elsevier, vol. 141(1), pages 44-64, November.
  13. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, Elsevier, vol. 173(1), pages 83-107.

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