We consider the generalized state space model (GSSM) which is an extension of the state space model to the non-Gaussian and non-linear model. There are serious problems in the GSSM approach because of the need for numerical integration over a state space. A Monte Carlo method for filtering and smoothing, called the Monte Carlo Filter (MCF), has been proposed to overcome this numerical problem. It has been pointed out that there exists a close relationship between the MCF and the genetic algorithm (GA) and that an essential structure involved in the MCF is quite similar to that in the GA. In this study, we try to replace the step of the prediction by the mutation and crossover operators in the GA, and demonstrate their performance as the system noise. We furthermore propose a smoothing algorithm in which a massively simple parallel procedure plays an important role. The proposed method is first applied to a simple problem and then to a seasonal adjustment for quarterly data sets in order to illustrate its broad applicability.
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