An investigation into the effects and effectiveness of correlation network filtration methods with financial returns

When studying financial markets, we often look at estimating a correlation matrix from asset returns. These tend to be noisy, with many more dimensions than samples, so often the resulting correlation matrix is filtered. Popular methods to do this include the minimum spanning tree, planar maximally filtered graph and the triangulated maximally filtered graph, which involve using the correlation network as the adjacency matrix of a graph and then using tools from graph theory. These assume the data fits some form of shape. We do not necessarily have a reason to believe that the data does fit into this shape, and there have been few empirical investigations comparing how the methods perform. In this paper we look at how the filtered networks are changed from the original networks using stock returns from the US, UK, German, Indian and Chinese markets, and at how these methods affect our ability to distinguish between datasets created from different correlation matrices using a graph embedding algorithm. We find that the relationship between the full and filtered networks depends on the data and the state of the market, and decreases as we increase the size of networks, and that the filtered networks do not provide an improvement in classification accuracy compared to the full networks.