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

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  • Jonathan B. Hill

    ()
    (Department of Economics, Florida International University)

Abstract

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
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Bibliographic Info

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

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Keywords: Orthogonal decompositions; Banach spaces; projection iterations; infinite variance; moving average; nonlinear impulse response function; smooth transition autoregression; Lp-metric projection; Lp-GMM.;

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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. 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.
  3. Gourieroux, Christian & Jasiak, Joanna, 1999. "Nonlinear innovations and impulse responses," CEPREMAP Working Papers (Couverture Orange) 9906, CEPREMAP.
  4. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
  5. 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.
  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. 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.
  9. 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.
  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. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
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Cited by:
  1. Jonathan Hill, 2006. "Asymptotically Nuisance-Parameter-Free Consistent Tests of Lp-Functional Form," Working Papers 0608, Florida International University, Department of Economics.
  2. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.

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