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Nonlinear Innovations and Impulse Response

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  • Christian Gourieroux

    (Crest)

  • Joanna Jasiak

    (Crest)

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.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 99-44.

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Date of creation: 1999
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Handle: RePEc:crs:wpaper:99-44

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  1. 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.
  2. 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.
  3. Qiwei Yao & Howell Tong, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics 19426, London School of Economics and Political Science, LSE Library.
  4. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbance," Working papers 497, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 127-157, November.
  6. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-52, September.
  7. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc.
  8. 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.
  9. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  10. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
  11. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  12. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  13. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  14. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
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Cited by:
  1. Andrew Chesher & Geert Dhaene & Christian Gourieroux & Olivier Scaillet, 1999. "Bartlett Identities Tests," Working Papers 99-32, Centre de Recherche en Economie et Statistique.
  2. Joann Jasiak, 1996. "Persistence in Intertrade Durations," Working Papers 1999_8, York University, Department of Economics, revised Mar 1999.
  3. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers 2000-05, Centre de Recherche en Economie et Statistique.
  4. Jardet, C. & Monfort, A. & Pegoraro, F., 2009. "New Information Response Functions," Working papers 235, Banque de France.
  5. 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.
    • Lars Peter Hansen & Jaroslav Borovicka & Mark Hendricks & Jose A. Scheinkman, 2010. "Risk Price Dynamics," Working Papers 2010-004, Becker Friedman Institute for Research In Economics.
    • Jaroslav Borovička & Lars Peter Hansen & Mark Hendricks & José A. Scheinkman, 2009. "Risk Price Dynamics," NBER Working Papers 15506, National Bureau of Economic Research, Inc.
  6. 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.
  7. Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes," Econometrics 0401001, EconWPA, revised 22 Apr 2004.

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