Strong Orthogonal Decompositions and Nonlinear Impulse Response Functions for Infinite-Variance Processes
AbstractIn 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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Bibliographic InfoPaper provided by Florida International University, Department of Economics in its series Working Papers with number 0408.
Length: 37 pages
Date of creation: May 2004
Date of revision:
Orthogonal decompositions; Banach spaces; projection iterations; infinite variance; moving average; nonlinear impulse response function; smooth transition autoregression; Lp-metric projection; Lp-GMM.;
Other versions of this item:
- Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes," Econometrics 0401001, EconWPA, revised 22 Apr 2004.
- 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-2005-08-13 (All new papers)
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