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Aspects of prediction

Part of: Statistics Probability theory and stochastic processes

Published online by Cambridge University Press:  30 March 2016

N. H. Bingham  and
Badr Missaoui
N. H. Bingham
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. Email address: n.bingham@imperial.ac.uk.
Badr Missaoui
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. Email address: badr.missaoui08@imperial.ac.uk.
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Abstract

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We survey some aspects of the classical prediction theory for stationary processes, in discrete time in Section 1, turning in Section 2 to continuous time, with particular reference to reproducing-kernel Hilbert spaces and the sampling theorem. We discuss the discrete-continuous theories of ARMA-CARMA, GARCH-COGARCH, and OPUC-COPUC in Section 3. We compare the various models treated in Section 4 by how well they model volatility, in particular volatility clustering. We discuss the infinite-dimensional case in Section 5, and turn briefly to applications in Section 6.

Keywords

Stationary processKolmogorov isomorphism theoremtime seriesstochastic volatilityvolatility clusteringBanach spacecovariance operatorlocally convexreproducing-kernel Hilbert spacesampling theorem

MSC classification

Primary: 60-02: Research exposition (monographs, survey articles)
Secondary: 62-02: Research exposition (monographs, survey articles)
Type
Part 5. Finance and econometrics
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 189 - 201
Copyright
Copyright © Applied Probability Trust 2014 

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