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Testing Granger Non-Causality in Expectiles

Author

Listed:
  • Taoufik Bouezmarni

    (Universite de Sherbrooke)

  • Mohamed Doukali

    (School of Economics, University of East Anglia)

  • Abderrahim Taamouti

    (University of Liverpool)

Abstract

This paper aims to derive a consistent test of Granger causality at a given expectile. We also propose a sup Wald test for jointly testing Granger causality at all expectiles that has the correct asymptotic size and power properties. Expectiles have the advantage of capturing similar information as quantiles, but they also have the merit of being much more straightforward to use than quantiles, since they are defined as least squares analogue of quantiles. Studying Granger causality in expectiles is practically simpler and allows us to examine the causality at all levels of the conditional distribution. Moreover, testing Granger causality at all expectiles provides a su¢ cient condition for testing Granger causality in distribution. A Monte Carlo simulation study reveals that our tests have good finite-sample size and power properties for a variety of data-generating processes and di¤erent sample sizes. Finally, we provide two empirical applications to illustrate the usefulness of the proposed tests.

Suggested Citation

  • Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2023. "Testing Granger Non-Causality in Expectiles," University of East Anglia School of Economics Working Paper Series 2023-02, School of Economics, University of East Anglia, Norwich, UK..
    • Handle: RePEc:uea:ueaeco:2023-02
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    References listed on IDEAS

    as
    1. Zheng Yang & Anthony H. Tu & Yong Zeng, 2014. "Dynamic linkages between Asian stock prices and exchange rates: new evidence from causality in quantiles," Applied Economics, Taylor & Francis Journals, vol. 46(11), pages 1184-1201, April.
    2. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    3. Taoufik Bouezmarni & Abderrahim Taamouti, 2014. "Nonparametric tests for conditional independence using conditional distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 697-719, December.
    4. 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.
    5. Baur, Dirk G. & Dimpfl, Thomas & Jung, Robert C., 2012. "Stock return autocorrelations revisited: A quantile regression approach," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 254-265.
    6. Freddy Delbaen, 2013. "A Remark on the Structure of Expectiles," Papers 1307.5881, arXiv.org.
    7. Boudjellaba, Hafida & Dufour, Jean-Marie & Roy, Roch, 1994. "Simplified conditions for noncausality between vectors in multivariate ARMA models," Journal of Econometrics, Elsevier, vol. 63(1), pages 271-287, July.
    8. Tae-Hwy Lee & Weiping Yang, 2012. "Money–Income Granger-Causality in Quantiles," Advances in Econometrics, in: 30th Anniversary Edition, pages 385-409, Emerald Group Publishing Limited.
    9. Chuang, Chia-Chang & Kuan, Chung-Ming & Lin, Hsin-Yi, 2009. "Causality in quantiles and dynamic stock return-volume relations," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1351-1360, July.
    10. Chow, Edward H & Lee, Wayne Y & Solt, Michael E, 1997. "The Exchange-Rate Risk Exposure of Asset Returns," The Journal of Business, University of Chicago Press, vol. 70(1), pages 105-123, January.
    11. Abdelaati Daouia & Stéphane Girard & Gilles Stupfler, 2018. "Estimation of tail risk based on extreme expectiles," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 263-292, March.
    12. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    13. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
    16. repec:taf:jnlbes:v:30:y:2012:i:2:p:275-287 is not listed on IDEAS
    17. Fabio Bellini & Elena Di Bernardino, 2017. "Risk management with expectiles," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 487-506, May.
    18. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    19. Belkacem Abdous & Bruno Remillard, 1995. "Relating quantiles and expectiles under weighted-symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 371-384, June.
    20. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    21. Jeong, Kiho & Härdle, Wolfgang K. & Song, Song, 2012. "A Consistent Nonparametric Test For Causality In Quantile," Econometric Theory, Cambridge University Press, vol. 28(4), pages 861-887, August.
    22. Griffin, John M & Stulz, Rene M, 2001. "International Competition and Exchange Rate Shocks: A Cross-Country Industry Analysis of Stock Returns," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 215-241.
    23. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    24. 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.
    25. Johanna F. Ziegel, 2016. "Coherence And Elicitability," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 901-918, October.
    26. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(4), pages 829-864, August.
    27. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2014. "Nonparametric estimation and inference for conditional density based Granger causality measures," Journal of Econometrics, Elsevier, vol. 180(2), pages 251-264.
    28. Xiaojun Song & Abderrahim Taamouti, 2018. "Measuring Nonlinear Granger Causality in Mean," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 321-333, April.
    29. Abdelaati Daouia & Irène Gijbels & Gilles Stupfler, 2019. "Extremiles: A New Perspective on Asymmetric Least Squares," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1366-1381, July.
    30. Numan Ülkü & Olena Onishchenko, 2019. "Trading volume and prediction of stock return reversals: Conditioning on investor types' trading," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 38(6), pages 582-599, September.
    31. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    32. Volker Krätschmer & Henryk Zähle, 2017. "Statistical Inference for Expectile-based Risk Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 425-454, June.
    33. Schnabel, Sabine K. & Eilers, Paul H.C., 2009. "Optimal expectile smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4168-4177, October.
    34. Victor Troster, 2018. "Testing for Granger-causality in quantiles," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 850-866, September.
    35. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    36. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    37. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
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    More about this item

    Keywords

    Granger causality in expectiles; Granger causality in distribution; expectile regression function; asymmetric loss function; sup-Wald test.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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