Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation

Vidoni Paolo ()
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Vidoni Paolo: University of Udine

Studies in Nonlinear Dynamics & Econometrics, 2004, vol. 8, issue 2, 20

Abstract: State space models provide a useful stochastic description for dynamic phenomena, based on unobserved or latent variables. When the model rests on linear and Gaussian assumptions there exists a well-known iterative procedure, called the Kalman filter, which gives analytic updating recursion for the filtering, the prediction and the smoothing distributions. However, this is rare and a state space model does not usually admit such a filter. For this reason, instead of looking for analytic solutions, a number of papers aim to define alternative procedures, giving numerical or approximate solutions. This paper concerns a particular class of models based on the assumption that the mixed process, obtained by alternating states and observations, is a Markov process. The main features of this class of models, proposed for stochastic volatility description by Barndorff-Nielsen (1997), are emphasized. In this framework, some new non-linear Gaussian state space models, computationally tractable and of potential interest for applications, may be defined.

Date: 2004
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DOI: 10.2202/1558-3708.1213

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