A method for detection of abrupt changes in the financial market combining wavelet decomposition and correlation graphs

The objective of this work is to propose a new methodology to detect the imminence of abrupt changes in the stock market by combining a numerical indicator based on the wavelet decomposition technique with a measure of the interdependency of the markets using graph theory. While the indicator based on wavelet decomposition is based on a single time series, an approach based on network representation can provide information on the interdependency of the various markets. More specifically, the stock market indices are associated with nodes of a network and the correlation between pairs of nodes with links. Results from the theory of graphs can then be used to indicate numerically the connectivity of this network. Experimentations with a variety of financial time series shows that the connectivity varies as trends of the financial time series varies. Combining the indicator based on the wavelet decomposition with the proposed measure of the connectivity of the network, it was possible to refine the authors previous results in terms of detecting abrupt changes in the stock market. In order to illustrate the methodology a case study involving twelve stock market indices was presented.