Extremum Monte Carlo Filters: Real-Time Signal Extraction via Simulation and Regression

This paper introduces a novel simulation-based filtering method for general state space models. It allows for the computation of time-varying conditional means, quantiles, and modes, but also for the prediction of latent variables in general. The method relies on generating artificial samples of data from the joint distribution implied by the model and on estimating the conditional quantities of interest via extremum estimation. We call this procedure Extremum Monte Carlo and define a corresponding class of filters for signal extraction. The method can be applied to any model from which data can be simulated and is not liable to the curse of dimensionality. Furthermore, the use of extremum estimation allows for a wide range of conditioning sets, including data with missing entries and unequal spacing. The filtering method also places the computational burden predominantly in the off-line phase, which makes it particularly suitable for real-time applications. We present illustrations for some challenging problems characterized by nonlinearity, high-dimensionality, and intractable density functions.