Correlations in finance:: a statistical approach

The behaviour of stock markets has been modelled actively during recent years. In some cases the market is modelled as a whole through the time series analysis of some indexes. But the market is made of companies whose time series can be studied independently. In this paper we have paid attention to the characterization of correlations and covariance among different companies in order to extract information about the market. We have used a statistical technique based on the analysis of the covariance matrix between the indexes of companies. When taking into account the sampling uncertainties and high order cumulants of index probability distribution, it is possible to classify automatically trends or clusters of companies in order to identify some independent "submarkets". The method is applied to some finance data sets coming from the Spanish financial market IBEX35.