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Strong Orthogonal Decompositions and Nonlinear Impulse Response Functions for Infinite-Variance Processes

  • Jonathan B. Hill

    ()

    (Department of Economics, Florida International University)

In this paper we prove Wold-type decompositions with strongorthogonal prediction innovations exist in smooth, re‡exive Banach spaces of discrete time processes if and only if the projection operator generating the innovations satisfies the property of iterations. Our theory includes as special cases all previous Wold-type decompositions of discrete time processes; completely characterizes when nonlinear heavy-tailed processes obtain a strong-orthogonal moving average representation; and easily promotes a theory of nonlinear impulse response functions for infinite variance processes. We exemplify our theory by developing a nonlinear impulse response func tion for smooth transition threshold processes, we discuss how to test de composition innovations for strong orthogonality and whether the proposed model represents the best predictor, and we apply the methodology to currency exchange rates.

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File URL: http://casgroup.fiu.edu/pages/docs/2245/1280267958_04-08.pdf
File Function: Revised version, 2006
Download Restriction: no

Paper provided by Florida International University, Department of Economics in its series Working Papers with number 0408.

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Length: 37 pages
Date of creation: May 2004
Date of revision:
Handle: RePEc:fiu:wpaper:0408
Contact details of provider: Postal: Miami, FL 33199
Phone: (305) 348-2316
Fax: (305) 348-1524
Web page: http://casgroup.fiu.edu/Economics/
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  1. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  2. Christian Gourieroux & Joanna Jasiak, 1999. "Nonlinear Innovations and Impulse Response," Working Papers 99-44, Centre de Recherche en Economie et Statistique.
  3. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
  4. Simon M. Potter, 1999. "Nonlinear impulse response functions," Staff Reports 65, Federal Reserve Bank of New York.
  5. 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.
  6. Falk, Barry L. & Wang, Chun-Hsuan, 2003. "Testing Long-Run Ppp with Infinite-Variance Returns," Staff General Research Papers 10323, Iowa State University, Department of Economics.
  7. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
  8. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
  9. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  10. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  11. Lin, Wen-Ling, 1997. "Impulse Response Function for Conditional Volatility in GARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 15-25, January.
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