Expected a posteriori estimation in financial applications
This paper introduces a new method for online estimation and prediction of states and parameters of nonlinear stochastic differential equations. In this setup parameters are considered as random variables in a Bayesian sense, which requires integration over parameter distributions. This is accomplished by well suited quadratures. The suggested procedure is incorporated into a state space architecture, which allows for sequential calculation of likelihood functions. This is done by normal correlation updates and prediction error decomposition. The resulting EAP-Filter can process a variety of nonlinear problems, including latent states. Additionally, estimates and predictions for system states and parameters can be calculated online, without iterative loops.
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