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Sample Covariance Shrinkage for High Dimensional Dependent Data

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  • Sancetta, A.

Abstract

For high dimensional data sets the sample covariance matrix is usually unbiased but noisy if the sample is not large enough. Shrinking the sample covariance towards a constrained, low dimensional estimator can be used to mitigate the sample variability. By doing so, we introduce bias, but reduce variance. In this paper, we give details on feasible optimal shrinkage allowing for time series dependent observations.

Suggested Citation

  • Sancetta, A., 2006. "Sample Covariance Shrinkage for High Dimensional Dependent Data," Cambridge Working Papers in Economics 0637, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0637
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    3. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    4. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
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    Cited by:

    1. repec:eee:spapps:v:128:y:2018:i:8:p:2816-2855 is not listed on IDEAS
    2. Bernardini, Emmanuela & Cubadda, Gianluca, 2015. "Macroeconomic forecasting and structural analysis through regularized reduced-rank regression," International Journal of Forecasting, Elsevier, vol. 31(3), pages 682-691.
    3. Sancetta, Alessio, 2013. "Weak conditions for shrinking multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 285-300.
    4. repec:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1040-y is not listed on IDEAS
    5. repec:taf:jnlasa:v:112:y:2017:i:517:p:424-435 is not listed on IDEAS
    6. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.

    More about this item

    Keywords

    Sample Covariance Matrix; Shrinkage; Weak Dependence;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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