Advanced Search
MyIDEAS: Login

A Nonparametric Copula Based Test for Conditional Independence with Applications to Granger Causality

Contents:

Author Info

  • Taoufik Bouezmarni
  • Jeroen Rombouts

    ()

  • Abderrahim Taamouti

Abstract

This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables. Le présent document propose un nouveau test non paramétrique d’indépendance conditionnelle, lequel est fondé sur la comparaison des densités de la copule de Bernstein suivant la distance de Hellinger. Le test est facile à réaliser, du fait qu’il n’implique pas de fonction de pondération dans les variables utilisées et peut être appliqué dans des conditions générales puisqu’il n’y a pas de restriction sur l’étendue des données. En fait, dans le cas de la copule non paramétrique, l’application du test ne requiert qu’une largeur de bande. Nous démontrons que les variables utilisées pour le test jouent asymptotiquement un rôle crucial sous l’hypothèse nulle. Nous établissons aussi les propriétés des pouvoirs locaux et justifions la validité de la technique bootstrap (technique d’auto-amorçage) que nous utilisons dans les contextes où les échantillons sont de taille finie. Une étude par simulation illustre l’ampleur adéquate et la puissance du test. Nous démontrons la pertinence empirique de notre démarche en mettant l’accent sur les liens de causalité de Granger et en recourant à des séries temporelles de données financières pour vérifier l’effet de levier non linéaire, par opposition à l’effet de rétroaction de la volatilité, et la causalité entre le rendement des actions et le volume des transactions. Dans une troisième application, nous examinons les liens de causalité de Granger entre certaines variables macroéconomiques.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.cirano.qc.ca/pdf/publication/2009s-28.pdf
Download Restriction: no

Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2009s-28.

as in new window
Length:
Date of creation: 01 Jun 2009
Date of revision:
Handle: RePEc:cir:cirwor:2009s-28

Contact details of provider:
Postal: 2020 rue University, 25e étage, Montréal, Quéc, H3A 2A5
Phone: (514) 985-4000
Fax: (514) 985-4039
Email:
Web page: http://www.cirano.qc.ca/
More information through EDIRC

Related research

Keywords: Nonparametric tests; conditional independence; Granger non-causality; Bernstein density copula; bootstrap; finance; volatility asymmetry; leverage effect; volatility feedback effect; macroeconomics; tests non paramétriques; indépendance conditionnelle; non-causalité de Granger; copule de densité de Bernstein; bootstrap; finance; asymétrie de la volatilité; effet de levier; effet de rétroaction de la volatilité; macroéconomie.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 353-384.
  2. Qi Li & Esfandiar Maasoumi & Jeffrey S. Racine, 2008. "A Nonparametric Test for Equality of Distributions with Mixed Categorical and Continuous Data," Emory Economics 0805, Department of Economics, Emory University (Atlanta).
  3. Sokbae 'Simon' Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Gouriéroux, Christian & Tenreiro, Carlos, 2001. "Local Power Properties of Kernel Based Goodness of Fit Tests," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 161-190, August.
  5. Simon Gervais & Ron Kaniel & Dan Mingelgrin, . "The High Volume Return Premium," Rodney L. White Center for Financial Research Working Papers 1-99, Wharton School Rodney L. White Center for Financial Research.
  6. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
  7. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  8. Ben Bernanke, 1990. "The Federal Funds Rate and the Channels of Monetary Transnission," NBER Working Papers 3487, National Bureau of Economic Research, Inc.
  9. Pindyck, Robert S, 1984. "Risk, Inflation, and the Stock Market," American Economic Review, American Economic Association, vol. 74(3), pages 335-51, June.
  10. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(06), pages 1016-1041, December.
  11. Karim Chalak & Halbert White, 2008. "Causality, Conditional Independence, and Graphical Separation in Settable Systems," Boston College Working Papers in Economics 689, Boston College Department of Economics, revised 04 Jul 2010.
  12. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen VK & TAAMOUTI, Abderrahim, . "Asymptotic properties of the Bernstein density copula estimator for alpha-mixing data," CORE Discussion Papers RP -2302, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Jean-Marie Dufour & René García & Abderrahim Taamouti, 2008. "Measuring causality between volatility and returns with high-frequency data," Economics Working Papers we084422, Universidad Carlos III, Departamento de Economía.
  14. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-21, March.
  15. Bernanke, Ben S. & Mihov, Ilian, 1995. "Measuring Monetary Policy," Economics Series 10, Institute for Advanced Studies.
  16. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June.
  17. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Estimating quadratic variation using realised variance," Economics Series Working Papers 2001-W20, University of Oxford, Department of Economics.
  18. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
  19. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  20. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  21. Christopher M. Turner & Richard Startz & Charles R. Nelson, 1989. "A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market," NBER Working Papers 2818, National Bureau of Economic Research, Inc.
  22. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
  23. Turner, C.M. & Startz, R. & Nelson, C.R., 1989. "The Markov Model Of Heteroskedasticity, Risk And Learning In The Stock Market," Discussion Papers in Economics at the University of Washington 89-01, Department of Economics at the University of Washington.
  24. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  25. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-52, September.
  26. Christopher A. Sims, 1980. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered," NBER Working Papers 0430, National Bureau of Economic Research, Inc.
  27. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  28. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  29. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  30. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  31. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  32. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  33. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March.
  34. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-91, May.
  35. Su, Liangjun & White, Halbert, 2003. "Testing Conditional Independence Via Empirical Likelihood," University of California at San Diego, Economics Working Paper Series qt35v8g0fm, Department of Economics, UC San Diego.
  36. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
  37. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
  38. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
  39. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  40. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
  41. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
  42. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
  43. 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.
  44. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  45. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  46. Hsiao, Cheng, 1982. "Autoregressive modeling and causal ordering of economic variables," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 243-259, November.
  47. Westerfield, Randolph, 1977. "The Distribution of Common Stock Price Changes: An Application of Transactions Time and Subordinated Stochastic Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(05), pages 743-765, December.
  48. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
  49. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  50. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  51. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  52. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Jesús Gonzalo & AbderrahimTaamouti, 2012. "The reaction of stock market returns to anticipated unemployment," Economics Working Papers we1237, Universidad Carlos III, Departamento de Economía.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2009s-28. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.