An exact smoother in a fuzzy jump Markov switching model

In this paper, we address the exact smoothing problem of Conditionally Gaussian Observed Markov Switching Model (CGOMSM). The proposed approach tackles the discontinuity feature in switching regime models by incorporating fuzzy switches instead of hard jumps. Fuzzy switched based approach is more adapted to real-world application in which regime continuity is an intrinsic property. We define, with respect to a measure, the local density of the switches and we show how fast smoothing equations should be adapted to cope with the fuzzy model. Finally, we show through several experiments the interest of the fuzzy switches model.