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Random Matrix Theory and Macro-Economic Time-Series: An Illustration Using the Evolution of Business Cycle Synchronisation, 1886-2006

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  • Ormerod, Paul

Abstract

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.

Suggested Citation

  • Ormerod, Paul, 2008. "Random Matrix Theory and Macro-Economic Time-Series: An Illustration Using the Evolution of Business Cycle Synchronisation, 1886-2006," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-10.
    • Handle: RePEc:zbw:ifweej:7374
    DOI: 10.5018/economics-ejournal.ja.2008-26
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    References listed on IDEAS

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    1. Martins, André C.R., 2007. "Random, but not so much a parameterization for the returns and correlation matrix of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 527-532.
    2. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    3. Plerou, V & Gopikrishnan, P & Rosenow, B & Amaral, L.A.N & Stanley, H.E, 2000. "A random matrix theory approach to financial cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 374-382.
    4. Andre C. R. Martins, 2007. "Random, but not so much: A parameterization for the returns and correlation matrix of financial time series," Papers physics/0701025, arXiv.org.
    5. Michael D. Bordo & Thomas Helbling, 2003. "Have National Business Cycles Become More Synchronized?," NBER Working Papers 10130, National Bureau of Economic Research, Inc.
    6. Ormerod, Paul & Mounfield, Craig, 2000. "Random matrix theory and the failure of macro-economic forecasts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 497-504.
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    Cited by:

    1. Thomas Lux & Duc Thi Luu & Boyan Yanovski, 2020. "An analysis of systemic risk in worldwide economic sentiment indices," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 47(4), pages 909-928, November.
    2. Luu, Duc Thi & Yanovski, Boyan & Lux, Thomas, 2018. "An analysis of systematic risk in worldwide econonomic sentiment indices," Economics Working Papers 2018-03, Christian-Albrechts-University of Kiel, Department of Economics.
    3. Duc Thi Luu, 2022. "Portfolio Correlations in the Bank-Firm Credit Market of Japan," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 529-569, August.

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    More about this item

    Keywords

    Random matrix theory; macroeconomic time-series data; international business cycle; synchronisation;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • N10 - Economic History - - Macroeconomics and Monetary Economics; Industrial Structure; Growth; Fluctuations - - - General, International, or Comparative

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