Journal of Applied Probability

Aspects of prediction

N. H. Bingham and Badr Missaoui


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.

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J. Appl. Probab., Volume 51A (2014), 189-201.

First available in Project Euclid: 2 December 2014

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Primary: 60-02: Research exposition (monographs, survey articles)
Secondary: 62-02: Research exposition (monographs, survey articles)

Stationary process Kolmogorov isomorphism theorem time series stochastic volatility volatility clustering Banach space covariance operator locally convex reproducing-kernel Hilbert space sampling theorem


Bingham, N. H.; Missaoui, Badr. Aspects of prediction. J. Appl. Probab. 51A (2014), 189--201. doi:10.1239/jap/1417528475.

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