State space modelling and simulation filter methods

摘要: We model a time series уt, t= 1,..., n, using a state space model. That is уt is conditionally independent given an unobserved su cient state at, which is itself assumed to be Markovian. The task will be to use simulation to estimate fa tjFt, t= 1,..., n, where Ft is contemperaneously available information. We assume parametric forms for both themeasurement'density f уtjat and thetransition'density of the state fa t+ 1jat. The state evolution is initialized by some density fa 0. Filtering can be thought of as the repeated application of the iteration fa t+ 1jFt+ 1 f уt+ 1jat+ 1