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

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  • Jonathan B. Hill

    (Florida International University)

Abstract

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.

Suggested Citation

  • Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes," Econometrics 0401001, University Library of Munich, Germany, revised 16 Dec 2005.
    • Handle: RePEc:wpa:wuwpem:0401001
    Note: Type of Document - pdf; prepared on WinXP; pages: 36
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0401/0401001.pdf
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    References listed on IDEAS

    as
    1. Jian Liu, 1989. "On The Existence Of A General Multiple Bilinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 341-355, July.
    2. 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.
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    Cited by:

    1. 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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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other

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