My bibliography  Save this paper

# A Consistent Characteristic-Function-Based Test for Conditional Independence

## Author

Listed:
• 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.

## Suggested Citation

• Su, Liangjun & White, Halbert, 2003. "A Consistent Characteristic-Function-Based Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series qt4dv0837f, Department of Economics, UC San Diego.
• Handle: RePEc:cdl:ucsdec:qt4dv0837f
as

File URL: http://www.escholarship.org/uc/item/4dv0837f.pdf;origin=repeccitec

## References listed on IDEAS

as
1. 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.
2. Sheedy, Elizabeth, 1998. "Correlation in currency markets a risk-adjusted perspective," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(1), pages 59-82, January.
3. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
4. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(04), pages 576-601, August.
5. Hjellvik, Vidar & Yao, Qiwei & Tjostheim, Dag, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
6. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
7. 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.
8. Lobato, Ignacio N, 2003. "Testing for Nonlinear Autoregression," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 164-173, January.
9. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
10. 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.
11. 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 339-368, July.
12. Efstathios Paparoditis & Dimitris Politis, 2000. "The Local Bootstrap for Kernel Estimators under General Dependence Conditions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 139-159, March.
13. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
14. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
Full references (including those not matched with items on IDEAS)

### Keywords

mixing; conditional characteristic function; Granger non-causality; non-parametric regression;

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cdl:ucsdec:qt4dv0837f. 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: (Lisa Schiff). General contact details of provider: http://edirc.repec.org/data/deucsus.html .

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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.