We investigate financial market correlations using random matrix theory and
principal component analysis. We use random matrix theory to demonstrate that
correlation matrices of asset price changes contain structure that is
incompatible with uncorrelated random price changes. We then identify the
principal components of these correlation matrices and demonstrate that a small
number of components accounts for a large proportion of the variability of the
markets that we consider.
We use techniques from network science to study correlations in the foreign
exchange (FX) market over the period 1991--2008. We consider an FX market
network in which each node represents an exchange rate and each weighted edge
represents a time-dependent correlation between the rates. To provide insights
into the clustering of the exchange rate time series, we investigate dynamic
communities in the network.