Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes
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.
|Date of creation:||06 Jan 2004|
|Date of revision:||16 Dec 2005|
|Note:||Type of Document - pdf; prepared on WinXP; pages: 36|
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- 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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