Prediction of ESTSP Competition Time Series by Unscented Kalman Filter and RTS Smoother

This article presents a solution to the time series prediction competition of the ESTSP 2007 conference. The solution is based on optimal filtering, which is a methodology for computing recursive solutions to statistical inverse problems, where a time varying stochastic state space model is measured through a sequence of noisy measurements. In the solution, the overall behavior of the time series is first modeled by constructing a linear state space model, which captures most of the visible features of the time series. Residual analysis techniques are then used for correcting the yet unmodeled features of the time series. These corrections result in a non-linear state space model, which is solved using a combination of linear Kalman filter, non-linear unscented Kalman filter and Rauch-TungStriebel smoother. The unknown parameters of the state space model are optimized to give the best possible prediction over 50 steps.