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A multiple testing approach to the regularisation of large sample correlation matrices

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  • Natalia Bailey
  • Vanessa Smith
  • M. Hashem Pesaran

Abstract

This paper proposes a novel regularisation method for the estimation of large covariance matrices, which makes use of insights from the multiple testing literature. The method tests the statistical significance of individual pair-wise correlations and sets to zero those elements that are not statistically significant, taking account of the multiple testing nature of the problem. The procedure is straightforward to implement, and does not require cross validation. By using the inverse of the normal distribution at a predetermined significance level, it circumvents the challenge of evaluating the theoretical constant arising in the rate of convergence of existing thresholding estimators. We compare the performance of our multiple testing (MT) estimator to a number of thresholding and shrinkage estimators in the literature in a detailed Monte Carlo simulation study. Results show that our MT estimator performs well in a number of different settings and tends to outperform other estimators, particularly when the cross-sectional dimension, N, is larger than the time series dimension, T IF the inverse covariance matrix is of interest then we recommend a shrinkage version of the MT estimator that ensures positive definiteness

Suggested Citation

  • Natalia Bailey & Vanessa Smith & M. Hashem Pesaran, 2014. "A multiple testing approach to the regularisation of large sample correlation matrices," Cambridge Working Papers in Economics 1413, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1413
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    Citations

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    Cited by:

    1. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2018. "Exponent of Cross-sectional Dependence for Residuals," CESifo Working Paper Series 7223, CESifo Group Munich.
    2. Natalia Bailey & Sean Holly & M. Hashem Pesaran, 2016. "A Two‐Stage Approach to Spatio‐Temporal Analysis with Strong and Weak Cross‐Sectional Dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 249-280, January.
    3. Chudik, Alexander & Pesaran, M. Hashem & Mohaddes, Kamiar, 2018. "Identifying Global and National Output and Fiscal Policy Shocks Using a GVAR," Globalization Institute Working Papers 351, Federal Reserve Bank of Dallas.
    4. Alexander Chudik & M. Hashem Pesaran, 2016. "Theory And Practice Of Gvar Modelling," Journal of Economic Surveys, Wiley Blackwell, vol. 30(1), pages 165-197, February.
    5. Craig, Ben R. & Saldias Zambrana, Martin, 2016. "Spatial Dependence and Data-Driven Networks of International Banks," Working Papers (Old Series) 1627, Federal Reserve Bank of Cleveland.
    6. Elhorst, J. Paul & Gross, Marco & Tereanu, Eugen, 2018. "Spillovers in space and time: where spatial econometrics and Global VAR models meet," Working Paper Series 2134, European Central Bank.
    7. Chudik, Alexander & Kapetanios, George & Pesaran, M. Hashem, 2016. "Big data analytics: a new perspective," Globalization Institute Working Papers 268, Federal Reserve Bank of Dallas.
    8. Ambrogio Cesa-Bianchi & M. Hashem Pesaran & Alessandro Rebucci, 2018. "Uncertainty and Economic Activity: A Multi-Country Perspective," NBER Working Papers 24325, National Bureau of Economic Research, Inc.
    9. A. Chudik & G. Kapetanios & M. Hashem Pesaran, 2018. "A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models," Econometrica, Econometric Society, vol. 86(4), pages 1479-1512, July.
    10. Filippo di Mauro & Alexander Al-Haschimi & Stephane Dees & Martina Jancokova, 2014. "Linking Distress of Financial Institutions to Macrofinancial Shocks," EcoMod2014 6807, EcoMod.
    11. Yang, Cynthia Fan, 2017. "Common Factors and Spatial Dependence: An Application to US House Prices," MPRA Paper 89032, University Library of Munich, Germany, revised 20 Aug 2018.
    12. Chudik, Alexander & Grossman, Valerie & Pesaran, M. Hashem, 2016. "A multi-country approach to forecasting output growth using PMIs," Journal of Econometrics, Elsevier, vol. 192(2), pages 349-365.
    13. George Kapetanios & M. Hashem Pesaran & Simon Reese, 2018. "A Residual-based Threshold Method for Detection of Units that are Too Big to Fail in Large Factor Models," CESifo Working Paper Series 7401, CESifo Group Munich.

    More about this item

    Keywords

    Sparse correlation matrices; High-dimensional data; Multiple testing; Thresholding; Shrinkage;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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