Dynamics and Structure of a Set of Stocks

In this paper we combine the Symbolic Time Series methods (Daw et. al., 2003) with the nearest neighbour single linkage clustering algorithm (Mantegna, 1999) to describe dynamics and structure of a set of stocks. We start with a partition of the time series state space; we label each piece of the partition by a symbol and convert the original time series into a symbolic sequence. Then we introduce a metric distance between two symbolic time series that is used to construct a Minimal Spanning Tree permitting to compute an ultrametric distance. By analyzing the data, we derive a hierarchical organization. From this analysis we can detect different clusters of companies according to their proximity which correspond with their common behaviour. The obtained classification can be used to analyze deep relationships among different branch of economic activities and can be a tool in portfolio construction