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December 2014 Projective stochastic equations and nonlinear long memory
Ieva Grublytė, Donatas Surgailis
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Adv. in Appl. Probab. 46(4): 1084-1105 (December 2014). DOI: 10.1239/aap/1418396244

Abstract

A projective moving average {Xt, tZ} is a Bernoulli shift written as a backward martingale transform of the innovation sequence. We introduce a new class of nonlinear stochastic equations for projective moving averages, termed projective equations, involving a (nonlinear) kernel Q and a linear combination of projections of Xt on `intermediate' lagged innovation subspaces with given coefficients αi and βi,j. The class of such equations includes usual moving average processes and the Volterra series of the LARCH model. Solvability of projective equations is obtained using a recursive equality for projections of the solution Xt. We show that, under certain conditions on Q, αi, and βi,j, this solution exhibits covariance and distributional long memory, with fractional Brownian motion as the limit of the corresponding partial sums process.

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Ieva Grublytė. Donatas Surgailis. "Projective stochastic equations and nonlinear long memory." Adv. in Appl. Probab. 46 (4) 1084 - 1105, December 2014. https://doi.org/10.1239/aap/1418396244

Information

Published: December 2014
First available in Project Euclid: 12 December 2014

zbMATH: 1305.60026
MathSciNet: MR3290430
Digital Object Identifier: 10.1239/aap/1418396244

Subjects:
Primary: 60G10
Secondary: 60F17, 60H25

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 4 • December 2014
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