Microinformation, Nonlinear Filtering and Granularity

The recursive prediction and filtering formulas of the Kalman filter are difficult to implementin nonlinear state space models. For Gaussian linear state space models, or for models with qualitativestate variables, the recursive formulas of the filter require the updating of a finite number ofsummary statistics. However, in the general framework a function has to be updated, which makesthe approach computationally cumbersome. The aim of this paper is to consider the situation ofa large number n of individual measurements, the so-called microinformation, and to take advantageof the large cross-sectional size to get closed-form prediction and filtering formulas at order1=n.[...]