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Large dimension forecasting models and random singular value spectra

Author

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  • J.-P. Bouchaud

  • L. Laloux
  • M. A. Miceli
  • M. 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 Marčenko-Pastur distribution for the case of rectangular correlation matrices. We illustrate the interest of our method on a set of macroeconomic time series. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • J.-P. Bouchaud & L. Laloux & M. A. Miceli & M. Potters, 2007. "Large dimension forecasting models and random singular value spectra," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 201-207, January.
    • Handle: RePEc:spr:eurphb:v:55:y:2007:i:2:p:201-207
    DOI: 10.1140/epjb/e2006-00204-0
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    References listed on IDEAS

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    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    2. George Kapetanios, 2004. "A New Method for Determining the Number of Factors in Factor Models with Large Datasets," Working Papers 525, Queen Mary University of London, School of Economics and Finance.
    3. George Kapetanios, 2004. "A New Method for Determining the Number of Factors in Factor Models with Large Datasets," Working Papers 525, Queen Mary University of London, School of Economics and Finance.
    4. 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.
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    Citations

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    Cited by:

    1. Christoly Biely & Stefan Thurner, 2008. "Random matrix ensembles of time-lagged correlation matrices: derivation of eigenvalue spectra and analysis of financial time-series," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 705-722.
    2. Yongcheng Qi & Mengzi Xie, 2020. "Spectral Radii of Products of Random Rectangular Matrices," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2185-2212, December.
    3. Linda Margarita Medina Herrera & Ernesto Armando Pacheco Velazquez, 2013. "Spectral Analysis And Networks In Financial Correlation Matrices, Analisis Espectral Y Redes En Matrices De Correlacion Financiera," Revista Internacional Administracion & Finanzas, The Institute for Business and Finance Research, vol. 6(6), pages 15-28.
    4. Reigneron, Pierre-Alain & Allez, Romain & Bouchaud, Jean-Philippe, 2011. "Principal regression analysis and the index leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3026-3035.
    5. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
    6. Anna Bykhovskaya & Vadim Gorin, 2023. "High-Dimensional Canonical Correlation Analysis," Papers 2306.16393, arXiv.org, revised Jan 2025.
    7. Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Papers 1203.6228, arXiv.org, revised Jul 2012.
    8. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
    9. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    10. 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.
    11. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    12. Zeng, Xingyuan, 2017. "Limiting empirical distribution for eigenvalues of products of random rectangular matrices," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 33-40.
    13. Alejandro Rodriguez Dominguez, 2026. "Order-Constrained Spectral Causality for Multivariate Time Series," Papers 2601.01216, arXiv.org, revised Apr 2026.

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