Aspects of prediction. (December 2014)

• Record Type: Journal Article
• Authors: Bingham, N. H.; Missaoui, Badr
• Is Part Of: Journal of applied probability. Volume 51:Number A(2014)
• Page Start: 189
• Page End: 201
• Publication Date: 2014-12
• Subjects: Stationary process, -- Kolmogorov isomorphism theorem, -- time series, -- stochastic volatility, -- volatility clustering, -- Banach space, -- covariance operator, -- locally convex, -- reproducing-kernel Hilbert space, -- sampling theorem; 60-02, -- 62-02; 519.2
• DOI: 10.1239/jap/1417528475
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : 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.