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Large dimension forecasting models and random singular value spectra

Author

Listed:
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Laurent Laloux

    (Science & Finance, Capital Fund Management)

  • M. Augusta Miceli
  • Marc Potters

    (Science & Finance, Capital Fund Management)

Abstract

We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random matrices, and gives an explicit expression for the interval where singular values are expected in the absence of any true correlations between the variables under study. Our result can be seen as the natural generalization of the Mar?cenko-Pastur distribution for the case of rectangular correlation matrices. We illustrate the interest of our method on a set of macroeconomic time series.

Suggested Citation

  • Jean-Philippe Bouchaud & Laurent Laloux & M. Augusta Miceli & Marc Potters, 2005. "Large dimension forecasting models and random singular value spectra," Science & Finance (CFM) working paper archive 500066, Science & Finance, Capital Fund Management.
  • Handle: RePEc:sfi:sfiwpa:500066
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Burda, Z. & Görlich, A. & Jarosz, A. & Jurkiewicz, J., 2004. "Signal and noise in correlation matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 295-310.
    3. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    4. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    5. Bernanke, Ben S. & Boivin, Jean, 2003. "Monetary policy in a data-rich environment," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 525-546, April.
    6. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    7. Granger, Clive W. J., 2001. "Macroeconometrics - Past and future," Journal of Econometrics, Elsevier, vol. 100(1), pages 17-19, January.
    8. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    9. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
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    Cited by:

    1. Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Papers 1203.6228, arXiv.org, revised Jul 2012.
    2. Frank Fabozzi & Sergio Focardi & Caroline Jonas, 2008. "On the challenges in quantitative equity management," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 649-665.
    3. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.

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