Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes
AbstractIn 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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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0401001.
Length: 36 pages
Date of creation: 06 Jan 2004
Date of revision: 22 Apr 2004
Note: Type of Document - pdf; prepared on WinXP; pages: 36
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Other versions of this item:
- Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Nonlinear Impulse Response Functions for Infinite-Variance Processes," Working Papers 0408, Florida International University, Department of Economics.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-01-08 (All new papers)
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