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Kernel-based nonlinear canonical analysis and time reversibility

Author

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  • Darolles, Serge
  • Florens, Jean-Pierre
  • Gourieroux, Christian

Abstract

We consider a kernel-based approach to nonlinear canonical correlation analysis and its implementation for time series. We deduce a test procedure of the reversibility hypothesis. The method is applied to the analysis of stochastic differential equation from high-frequency data on stock returns.
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Suggested Citation

  • Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.
    • Handle: RePEc:eee:econom:v:119:y:2004:i:2:p:323-353
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    References listed on IDEAS

    as
    1. Christian Gourieroux & Joann Jasiak, 2011. "Nonlinear Persistence and Copersistence," Palgrave Macmillan Books, in: Greg N. Gregoriou & Razvan Pascalau (ed.), Nonlinear Financial Econometrics: Markov Switching Models, Persistence and Nonlinear Cointegration, chapter 4, pages 77-103, Palgrave Macmillan.
    2. Darolles, Serge & Gourieroux, Christian, 2001. "Truncated dynamics and estimation of diffusion equations," Journal of Econometrics, Elsevier, vol. 102(1), pages 1-22, May.
    3. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    4. Christian Gouriéroux & Joann Jasiak, 2002. "Nonlinear Autocorrelograms: an Application to Inter‐Trade Durations," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(2), pages 127-154, March.
    5. repec:crs:wpaper:9963 is not listed on IDEAS
    6. 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.
    7. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
    8. Florens, Jean-Pierre & Renault, Eric & Touzi, Nizar, 1998. "Testing For Embeddability By Stationary Reversible Continuous-Time Markov Processes," Econometric Theory, Cambridge University Press, vol. 14(6), pages 744-769, December.
    9. Serge Darolles & Jean-Paul Laurent, 2000. "Approximating payoffs and pricing formulas," Post-Print halshs-00678228, HAL.
    10. repec:adr:anecst:y:2000:i:60:p:09 is not listed on IDEAS
    11. Darolles, Serge & Laurent, Jean-Paul, 2000. "Approximating payoffs and pricing formulas," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1721-1746, October.
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    Citations

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    Cited by:

    1. Escanciano, Juan Carlos & Hoderlein, Stefan & Lewbel, Arthur & Linton, Oliver & Srisuma, Sorawoot, 2021. "Nonparametric Euler Equation Identification And Estimation," Econometric Theory, Cambridge University Press, vol. 37(5), pages 851-891, October.
    2. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
    3. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    4. Christian Gourieroux & Hung T. Nguyen & Songsak Sriboonchitta, 2017. "Nonparametric estimation of a scalar diffusion model from discrete time data: a survey," Annals of Operations Research, Springer, vol. 256(2), pages 203-219, September.
    5. repec:adr:anecst:y:2007:i:85:p:05 is not listed on IDEAS
    6. Xiaohong Chen & Lars Peter Hansen & Jos´e A. Scheinkman, 2005. "Principal Components and the Long Run," Levine's Bibliography 122247000000000997, UCLA Department of Economics.
    7. Tommaso Proietti, 2023. "Peaks, gaps, and time‐reversibility of economic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 43-68, January.
    8. Xiaohong Chen & Lars Peter Hansen & Jose Scheinkman, 2009. "Principal Components and Long Run Implications of Multivariate Diffusions," Cowles Foundation Discussion Papers 1694, Cowles Foundation for Research in Economics, Yale University.
    9. Zacharias Psaradakis, 2008. "Assessing Time‐Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
    10. Christian Gouriéroux & Eric Renault & Pascale Valery, 2007. "Diffusion Processes with Polynomial Eigenfunctions," Annals of Economics and Statistics, GENES, issue 85, pages 115-130.
    11. Shibin Zhang, 2023. "A copula spectral test for pairwise time reversibility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 705-729, October.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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