Deducing the multi-trader population driving a financial market

Abstract

We previously laid out a framework for predicting financial movements and pockets of predictability by deducing the heterogeneity in the multi-agent population in terms of trader types playing in an artificial financial market model. 1 This work explores extensions to this basic framework. We allow for more intelligent agents with a richer strategy set, and we no longer constrain the estimate for the heterogeneity over the agents to a probability space. We then introduce a scheme which accounts for models with a wide variety of agent types. We also discuss a mechanism for bias removal on the estimates of the relevant parameters.

Kalman Filtering in the Presence of State Space Equality Constraints

“…The augmented state now forces D k x D k to be equal to δ k exactly (i.e., with no noise term) at every iteration. 5 Let us now expand the equations for the Kalman Filter prediction and update to gain a stronger understanding of how the filter has changed.…”

“…Equality constrained Kalman Filtering also appears as a subroutine in the more general framework of inequality constrained Kalman Filtering. One method for extending an equality constrained filter to an inequality constrained filter would be to use an active set method (as in [5]).…”