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

  • Jonathan B. Hill

    (Florida International University)

In this paper we prove Wold-type decompositions with strong-orthogonal prediction innovations exist in smooth, reflexive 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 function for smooth transition threshold processes, we discuss how to test decomposition 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://128.118.178.162/eps/em/papers/0401/0401001.pdf
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Paper provided by EconWPA in its series Econometrics with number 0401001.

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Length: 36 pages
Date of creation: 06 Jan 2004
Date of revision: 22 Apr 2004
Handle: RePEc:wpa:wuwpem:0401001
Note: Type of Document - pdf; prepared on WinXP; pages: 36
Contact details of provider: Web page: http://128.118.178.162

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  1. 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.
  2. Gourieroux, Christian & Jasiak, Joanna, 1999. "Nonlinear innovations and impulse responses," CEPREMAP Working Papers (Couverture Orange) 9906, CEPREMAP.
  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. 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.
  5. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
  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. 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.
  8. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  9. 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.
  10. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  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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