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.

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.