Dynamics of cluster structure in financial correlation matrix

The correlation dimensions in the financial market are calculated and used as a measure to study the cluster structure in the correlation coefficient matrix. First, based on the existing model, we present a toy model. Using the model-generated data, we find that the clearer cluster structure corresponds to a smaller dimension. It implies that the correlation dimension can be used as a measure of the cluster structure in the correlation coefficient matrix. Finally, we use the algorithm to compute the clusters in the real market and verify the previous empirical evidence. The results show that the cluster structure in the financial correlation coefficient matrix may change with time. The correlation dimension is smaller after the financial crisis, indicating that the cluster structure is clearer after the financial crisis.