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Nonlinear innovations and impulse responses

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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.

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File URL: http://www.cepremap.fr/depot/couv_orange/co9906.ps
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Bibliographic Info

Paper provided by CEPREMAP in its series CEPREMAP Working Papers (Couverture Orange) with number 9906.

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Length: 37 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:cpm:cepmap:9906

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References

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  1. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 97-37, Wharton School Center for Financial Institutions, University of Pennsylvania.
  2. Bosq, D. & Guégan, D., 1995. "Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system," Statistics & Probability Letters, Elsevier, Elsevier, vol. 25(3), pages 201-212, November.
  3. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198773207, October.
  4. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, Econometric Society, vol. 63(2), pages 265-79, March.
  5. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 119-147, September.
  6. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, Elsevier, vol. 81(1), pages 127-157, November.
  7. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," NBER Working Papers 2737, National Bureau of Economic Research, Inc.
  8. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 115-127.
  9. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, Econometric Society, vol. 48(1), pages 1-48, January.
  10. Qiwei Yao & Howell Tong, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 19426, London School of Economics and Political Science, LSE Library.
  11. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521411462.
  12. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, American Economic Association, vol. 62(4), pages 540-52, September.
  13. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521423083.
  14. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1127-1162, September.
  15. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 318-334, September.
  16. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 871-907, July.
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Cited by:
  1. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers, Centre de Recherche en Economie et Statistique 2000-05, Centre de Recherche en Economie et Statistique.
  2. Caroline JARDET & Alain MONFORT & Fulvio PEGORARO, 2011. "No-arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth," Working Papers, Centre de Recherche en Economie et Statistique 2011-03, Centre de Recherche en Economie et Statistique.
  3. Chesher, Andrew & Dhaene, Geert & Gouriéroux, Christian & Scaillet, Olivier, 1999. "Bartlett Identities Tests," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 1999019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  4. Jardet, C. & Monfort, A. & Pegoraro, F., 2009. "New Information Response Functions," Working papers, Banque de France 235, Banque de France.
  5. Lars Peter Hansen & Jaroslav BoroviÄka & Mark Hendricks & Jose A. Scheinkman, 2010. "Risk Price Dynamics," Working Papers, Becker Friedman Institute for Research In Economics 2010-004, Becker Friedman Institute for Research In Economics.
  6. Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Nonlinear Impulse Response Functions for Infinite-Variance Processes," Working Papers, Florida International University, Department of Economics 0408, Florida International University, Department of Economics.
  7. Joann Jasiak, 1996. "Persistence in Intertrade Durations," Working Papers, York University, Department of Economics 1999_8, York University, Department of Economics, revised Mar 1999.

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