Improved unscented Kalman smoothing for stock volatility estimation
We introduce a novel approximate inference algorithm for non-linear dynamical systems. The algorithm is based upon expectation propagation and Gaussian quadrature. The first forward pass is strongly related to the unscented Kalman filter. It improves upon unscented Kalman filtering by only making Gaussian approximations in the latent and not in the observation space. Smoothed estimates can be found without inverting latent space dynamics and can be improved by iteration. Multiple forward and backward passes make it possible to improve local approximations and make them as consistent as possible. We demonstrate the validity of the approach with an interesting inference problem in stochastic stock volatility models. The traditional unscented Kalman filter is ill suited for this problem: it can be proven that the traditional filter effectively never updates prior beliefs. The novel algorithm gives good results and improves with iteration.