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Nonlinear innovations and impulse responses

Author

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  • Gourieroux, Christian
  • Jasiak, Joanna

Abstract

This paper introduces a concept of innovation for the analysis of nonlinear dynamics. We show that nonlinear processes can be represented as functions of current and lagged values of such innovations. The residuals from nonlinear dynamic models axe used to construct various specification tests. We define and study nonlinear impulse response functions to transitory and permanent shocks.

Suggested Citation

  • Gourieroux, Christian & Jasiak, Joanna, 1999. "Nonlinear innovations and impulse responses," CEPREMAP Working Papers (Couverture Orange) 9906, CEPREMAP.
    • Handle: RePEc:cpm:cepmap:9906
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    References listed on IDEAS

    as
    1. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083, January.
    2. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, "undated". "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
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    6. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    7. Bosq, D. & Guégan, D., 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Statistics & Probability Letters, Elsevier, vol. 25(3), pages 201-212, November.
    8. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    9. D. Bosq & Dominique Guegan, 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Post-Print halshs-00199345, HAL.
    10. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    11. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    12. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
    13. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
    14. 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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    Citations

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    Cited by:

    1. Karapanagiotidis, Paul, 2013. "Empirical evidence for nonlinearity and irreversibility of commodity futures prices," MPRA Paper 56801, University Library of Munich, Germany.
    2. Jaroslav Borovička & Mark Hendricks & José A. Scheinkman, 2011. "Risk-Price Dynamics," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 3-65, Winter.
      • Jaroslav Borovička & Lars Peter Hansen & Mark Hendricks & José A. Scheinkman, 2009. "Risk Price Dynamics," NBER Working Papers 15506, National Bureau of Economic Research, Inc.
      • Lars Peter Hansen & Jaroslav BoroviÄ ka & Mark Hendricks & José A. Scheinkman, 2010. "Risk Price Dynamics," Working Papers 2010-004, Becker Friedman Institute for Research In Economics.
      • Jaroslav Borovicka & Lars Peter Hansen & Mark Hendricks & Jose A. Scheinkman, 2009. "Risk Price Dynamics," Working Papers 1393, Princeton University, Department of Economics, Econometric Research Program..
    3. Caroline Jardet & Alain Monfort & Fulvio Pegoraro, 2009. "New Information Response Functions," Working papers 235, Banque de France.
    4. Karapanagiotidis, Paul, 2014. "Dynamic modeling of commodity futures prices," MPRA Paper 56805, University Library of Munich, Germany.
    5. Jardet, Caroline & Monfort, Alain & Pegoraro, Fulvio, 2013. "No-arbitrage Near-Cointegrated VAR(p) term structure models, term premia and GDP growth," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 389-402.
    6. repec:hum:wpaper:sfb649dp2011-087 is not listed on IDEAS
    7. Lars Hansen & Jaroslav Borovicka, 2013. "Robust preference expansions," 2013 Meeting Papers 1199, Society for Economic Dynamics.
    8. Jaroslav Borovička & Lars P. Hansen & Jose A. Scheinkman, 2014. "Shock Elasticities and Impulse Responses," NBER Working Papers 20104, National Bureau of Economic Research, Inc.
    9. Hujer Reinhard & Grammig Joachim & Kokot Stefan, 2000. "Time Varying Trade Intensities and the Deutsche Telekom IPO / Zeitvariable Handelsintensitaten und die Deutsche Telekom IPO," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 220(6), pages 689-714, December.
    10. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.

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    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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