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Large dimension forecasting models and random singular value spectra

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  • 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.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500066.

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Date of creation: Dec 2005
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Handle: RePEc:sfi:sfiwpa:500066

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  1. 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.
  2. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  3. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  4. Granger, Clive W. J., 2001. "Macroeconometrics - Past and future," Journal of Econometrics, Elsevier, vol. 100(1), pages 17-19, January.
  5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  6. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  7. 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.
  8. 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.
  9. Ben S. Bernanke & Jean Boivin, 2001. "Monetary Policy in a Data-Rich Environment," NBER Working Papers 8379, National Bureau of Economic Research, Inc.
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Cited by:
  1. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
  2. Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Papers 1203.6228, arXiv.org, revised Jul 2012.

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