Random matrix theory and macro-economic time-series : an illustration using the evolution of business cycle synchronisation, 1886 - 2006

The aim of this paper is to show that random matrix theory (RMT) can be a useful addition to the economist's tool-kit in the analysis of macro-economic time series data. A great deal of applied economic work relies upon empirical estimates of the correlation matrix. However due to the finite size of both the number of variables and the number of observations, a reliable determination of the correlation matrix may prove to be problematic. The structure of the correlation matrix may be dominated by noise rather than by true information. Random matrix theory was developed in physics to overcome this problem, and to enable true information in a matrix to be distinguished from noise. There is now a large literature in which it is applied successfully to financial markets and in particular to portfolio selection. The author illustrates the application of the technique to macro-economic time-series data. Specifically, the evolution of the convergence of the business cycle between the capitalist economies from the late 19th century to 2006. The results are not in sharp contrast with those in the literature obtained using approaches with which economists are more familiar. However, there are differences, which RMT enables us to clarify. -- Random matrix theory ; macroeconomic time-series data ; international business cycle ; synchronisation