Kalman filtering in the presence of State Space Equality Constraints

We discuss two separate techniques for Kalman Filtering in the presence of state space equality constraints. We then prove that despite the lack of similarity in their formulations, under certain conditions, the two methods result in mathematically equivalent constrained estimate structures. We conclude that the potential benefits of using equality constraints in Kalman Filtering often outweigh the computational costs, and as such, equality constraints, when present, should be enforced by way of one of these two methods

Deducing the Multi-Trader Population Driving a Financial Market

We previously laid out a framework for predicting financial movements and pockets of predictability by deducing the heterogeneity in the multi-agent population in temrs of trader types playing in an artificial financial market model [7]. 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

Constrained Kalman filtering and predicting behaviour in agent-based financial market models

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Kalman Filtering with Equality and Inequality State Constraints

Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address - however, constraints are rarely exploited for these applications. We define the Kalman Filter and discuss two different approaches to incorporating constraints. Each of these approaches are first applied to equality constraints and then extended to inequality constraints. We discuss methods for dealing with nonlinear constraints and for constraining the state prediction. Finally, some experiments are provided to indicate the usefulness of such methods

Deducing the multi-trader population driving a financial market

We have previously laid out a basic framework for predicting financial movements and pockets of predictability by tracking the distribution of a multi-trader population playing on an artificial financial market model. 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 distribution over these agents to a probability space. We then introduce a fusion scheme which accounts for multiple runs of randomly chosen sets of possible agent types. We also discuss a mechanism for bias removal on the estimates

Forecasting Financial Time Series using Artificial Market Models

We discuss the theoretical machinery involved in predicting financial market movements using an artificial market model which has been trained on real financial data. This approach to market prediction - in particular, forecasting financial time-series by training a third-party or 'black box' game on the financial data itself - was discussed by Johnson et al in [10] and [13] and was based on some encouraging prelimary investigations of the dollar-yen exchange rate, various individual stocks, and stock market indices (see[12] for more details also). However, the initial attempts lacked a clear formal methodology. Here we present a detailed methodology, using optimization techniques to build an estimate of the strategy distribution across the multi-trader population. In contrast to earlier attempts, we are able to present a systematic method for identifying 'pockets of predictability' in real-world markets. We find that as each pocket closes up, the black-box system needs to be 'reset'- which is equivalent to saying that the current probability estimates of the strategy allocation across the multi-trader population are no longer accurate. Instead, new probability estimates need to be obtained by iterative updating, until a new 'pocket of predictability' emerges and reliable prediction can resume