Title: Modeling networks of currency tick-data as continuous time graphical models
Authors: Jonas Hallgren - Royal Institute of Technology KTH (Sweden) [presenting]
Timo Koski - royal institute of technology (Sweden)
Abstract: Continuous time Bayesian networks (CTBNs) are graphical representations of the dependence structures between continuous time random processes with finite state spaces. We propose a method for learning the structure of the CTBNs using a causality measure based on Kullback-Leibler divergence. We introduce the causality matrix which can be seen as a generalized version of the covariance matrix. We give a mixed radix representation of the process that much facilitates the learning and simulation. A new graphical model for tick-by-tick financial data is proposed and estimated. The model is inspired by speech recognition applications and computes the state of the process using transformations to frequency domain. The suggested approach is able to learn the graphical structure of both the tick-data and of a simulated example. Neuroscientists proposed Integrated Information Theory (IIT) as a way of measuring the amount of consciousness in a system. By the use of information geometry, we relate the proposed causality measure to Integrated Information Theory. The suggested approach allows us to work with tick-data in an easy way where it is not necessary to take every tick into account separately. Because of this and the promising results, we consider the CTBN-approach be relevant for studying tick-by-tick data.