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Large dimension forecasting models and random singular value spectra

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  • Jean-Philippe Bouchaud
  • Laurent Laloux
  • M. Augusta Miceli
  • Marc Potters

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 Marcenko-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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  • Jean-Philippe Bouchaud & Laurent Laloux & M. Augusta Miceli & Marc Potters, 2005. "Large dimension forecasting models and random singular value spectra," Papers physics/0512090, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0512090
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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.
    3. 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.

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