Dresden 2003 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 2: Finanzm
ärkte und Risikomanagement II

AKSOE 2.1: Talk

Monday, March 24, 2003, 14:00–14:30, BAR/205

Construction of a state space embedding for time-dependent stock market — •Ferdinand Jamitzky and Wolfram Bunk — MPE Garching

Using methods from information dynamics and graph theory we present a construction algorithm for a state space embedding of multivariate time series. The embedding is unique in such a way that it is an isometric mapping of the (high-dimensional) minimal spanning tree and its derivatives of a given point set. As an example for the method we present an analysis of multivariate stock market data covering a time period of eleven years of day-to-day variations of stock prices and order volumes. By using a metric (based on either linear correlation or mutual information) the mutual relation of the data is represented as a point set in a high-dimensional state space. This point set is further analyzed by computing the so-called minimal spanning tree and the corresponding adjacency matrices of higher order. Finally, an embedding is sought that isometrically maps the minimal spanning tree and its higher order derivatives into a lower dimensional space by using an optimization algorithm. In the resulting projected state space the cluster dynamics of the stock titles can be visualized and investigated.