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Dynamic Large Spatial Covariance Matrix Estimation in Application to Semiparametric Model Construction via Variable Clustering: the SCE approach

  • Song Song
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    To better understand the spatial structure of large panels of economic and financial time series and provide a guideline for constructing semiparametric models, this paper first considers estimating a large spatial covariance matrix of the generalized $m$-dependent and $\beta$-mixing time series (with $J$ variables and $T$ observations) by hard thresholding regularization as long as ${{\log J \, \cx^*(\ct)}}/{T} = \Co(1)$ (the former scheme with some time dependence measure $\cx^*(\ct)$) or $\log J /{T} = \Co(1)$ (the latter scheme with some upper bounded mixing coefficient). We quantify the interplay between the estimators' consistency rate and the time dependence level, discuss an intuitive resampling scheme for threshold selection, and also prove a general cross-validation result justifying this. Given a consistently estimated covariance (correlation) matrix, by utilizing its natural links with graphical models and semiparametrics, after "screening" the (explanatory) variables, we implement a novel forward (and backward) label permutation procedure to cluster the "relevant" variables and construct the corresponding semiparametric model, which is further estimated by the groupwise dimension reduction method with sign constraints. We call this the SCE (screen - cluster - estimate) approach for modeling high dimensional data with complex spatial structure. Finally we apply this method to study the spatial structure of large panels of economic and financial time series and find the proper semiparametric structure for estimating the consumer price index (CPI) to illustrate its superiority over the linear models.

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    File URL: http://arxiv.org/pdf/1106.3921
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    Paper provided by arXiv.org in its series Papers with number 1106.3921.

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    Date of creation: Jun 2011
    Date of revision: Jun 2011
    Handle: RePEc:arx:papers:1106.3921
    Contact details of provider: Web page: http://arxiv.org/

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    1. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148 Elsevier.
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    7. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," SFB 649 Discussion Papers SFB649DP2011-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Xia, Yingcun, 2008. "A Multiple-Index Model and Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1631-1640.
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    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
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    12. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," Papers 1106.3915, arXiv.org.
    13. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
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