A Recursive Recomputation Approach for Smoothing in Nonlinear State–Space Modeling: An Attempt for Reducing Space Complexity
IEEE Transactions on Signal Processing
In this paper, we develop a new generic implementation scheme for numerical smoothing in nonlinear and Bayesian state-space modeling. Our new generic implementation scheme, which we call recursive recomputation scheme, reduces the space complexity from ( ) to ( log ), at the cost of (log ) times computation of filtering distributions in time complexity. This reduction is accomplished by employing carefully designed recursive recomputation. The Japanese stock market price time-series data with =
... -series data with = 956 is taken up as an instance to demonstrate advantage of the proposed scheme. The path-sampling particle smoother is implemented with the scheme to smooth the whole interval estimating the change of volatility. The number of particles is 3 000 000, and the whole interval is smoothed with 5.3-GB storage, accomplishing saving of storage by a factor of 1/20. The computed smoothing distribution is compared with the ones computed with the existing two other well-known smoothers, the forward-backward smoother and the smoother based on two-filter formula. It turns out that, among the three, ours is the only method which succeeded in computing a reliable and plausible smoothing distribution in the situation. Index Terms-Hidden Markov model, particle filter, smoothing, space complexity, state-space model.