  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 then characterize the time-evolving relationships
between the different assets by investigating the correlations between the
asset price time series and principal components. Using this approach, we
uncover notable changes that occurred in financial markets and identify the
assets that were significantly affected by these changes. We show in particular
that there was an increase in the strength of the relationships between several
different markets following the 2007--2008 credit and liquidity crisis.
