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Nonlinear Persistence and Copersistence

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  • Christian Gourieroux

    (Crest)

  • Joanna Jasiak

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Abstract

Theoretical research on long-term relationships between economic time series has a history that spans several decades during which various linear and nonlinear comovements were unveiled, such as the Phillips curve, and the purchasing power parity. In contrast, the econometric analysis of long-term relationships is much more recent, and has been conducted mainly in the linear framework. This is the case of the cointegration theory for nonstationary time series (see Granger, 1986; Engle and Granger, 1987; Johansen, 1998), and the codependence theory for stationary series (Gourieroux and Peaucelle, 1992; Engle and Kozicki, 1993; Kugler and Neusser, 1993). Under both approaches, the dynamics of the time series of interest (i.e. VAR model) as well as their long-term relationships are assumed to be linear.
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Suggested Citation

  • Christian Gourieroux & Joanna Jasiak, 1999. "Nonlinear Persistence and Copersistence," Working Papers 99-63, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:99-63
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    1. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    2. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    4. repec:bla:ecorec:v:69:y:1993:i:206:p:233-38 is not listed on IDEAS
    5. 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.
    6. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    8. C. W. J. Granger & Jeff Hallman, 1991. "Nonlinear Transformations Of Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(3), pages 207-224, May.
    9. Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August.
    10. Kugler, Peter & Neusser, K, 1993. "International Real Interest Rate Equalization: A Multivariate Time-Series Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(2), pages 163-174, April-Jun.
    11. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    12. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
    13. 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.
    14. Abadir, Karim M. & Talmain, Gabriel, 2005. "Autocovariance functions of series and of their transforms," Journal of Econometrics, Elsevier, vol. 124(2), pages 227-252, February.
    15. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    16. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
    17. Serge Darolles & Jean-Pierre Florens & Christian Gourieroux, 1998. "Kernel Based Nonlinear Canonical Analysis," Working Papers 98-55, Center for Research in Economics and Statistics.
    18. Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
    19. He, Changli & Teräsvirta, Timo, 1997. "Statistical Properties of the Asymmetric Power ARCH Process," SSE/EFI Working Paper Series in Economics and Finance 199, Stockholm School of Economics, revised 30 Sep 1997.
    20. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    21. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    22. Engle, Robert F. & Issler, João Victor, 1993. "Common trends and common cycles in Latin America," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 47(2), April.
    23. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    24. Anderson, Heather M. & Vahid, Farshid, 1998. "Testing multiple equation systems for common nonlinear components," Journal of Econometrics, Elsevier, vol. 84(1), pages 1-36, May.
    25. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 686-710, August.
    26. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    27. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    28. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
    29. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
    30. Peter Kugler, 1990. "International Real Interest Rate Equalization: A Multivariate Time Series Approach," Diskussionsschriften dp9007, Universitaet Bern, Departement Volkswirtschaft.
    31. 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.
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    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Non-linear Functions of Non-Stationary Data Can be Stationary
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-02-27 03:17:00

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    2. 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.

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