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Dynamic Covariance Models

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  • Ziqi Chen
  • Chenlei Leng
Abstract
An important problem in contemporary statistics is to understand the relationship among a large number of variables based on a dataset, usually with p, the number of the variables, much larger than n, the sample size. Recent efforts have focused on modeling static covariance matrices where pairwise covariances are considered invariant. In many real systems, however, these pairwise relations often change. To characterize the changing correlations in a high-dimensional system, we study a class of dynamic covariance models (DCMs) assumed to be sparse, and investigate for the first time a unified theory for understanding their nonasymptotic error rates and model selection properties. In particular, in the challenging high-dimensional regime, we highlight a new uniform consistency theory in which the sample size can be seen as n4/5 when the bandwidth parameter is chosen as h∝n− 1/5 for accounting for the dynamics. We show that this result holds uniformly over a range of the variable used for modeling the dynamics. The convergence rate bears the mark of the familiar bias-variance trade-off in the kernel smoothing literature. We illustrate the results with simulations and the analysis of a neuroimaging dataset. Supplementary materials for this article are available online.

Suggested Citation

  • Ziqi Chen & Chenlei Leng, 2016. "Dynamic Covariance Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1196-1207, July.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:515:p:1196-1207
    DOI: 10.1080/01621459.2015.1077712
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    References listed on IDEAS

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    Cited by:

    1. Jian Zhang & Jie Li, 2022. "Factorized estimation of high‐dimensional nonparametric covariance models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 542-567, June.
    2. Ruijun Bu & Degui Li & Oliver Linton & Hanchao Wang, 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Working Papers 202212, University of Liverpool, Department of Economics.
    3. Xinyang Yu & Cheng Wang & Zhongqing Yang & Binyan Jiang, 2022. "Tuning selection for two-scale kernel density estimators," Computational Statistics, Springer, vol. 37(5), pages 2231-2247, November.
    4. Chen, Ziqi & Hu, Jianhua & Zhu, Hongtu, 2020. "Surface functional models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    5. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    6. Chen, Jia & Li, Degui & Linton, Oliver, 2019. "A new semiparametric estimation approach for large dynamic covariance matrices with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 212(1), pages 155-176.
    7. Ge, S. & Li, S. & Linton, O. B. & Liu, W. & Su, W., 2024. "Should We Augment Large Covariance Matrix Estimation with Auxiliary Network Information?," Janeway Institute Working Papers 2416, Faculty of Economics, University of Cambridge.
    8. Ge, S. & Li, S. & Linton, O. B. & Liu, W. & Su, W., 2024. "Should We Augment Large Covariance Matrix Estimation with Auxiliary Network Information?," Cambridge Working Papers in Economics 2427, Faculty of Economics, University of Cambridge.
    9. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
    10. Bu, R. & Li, D. & Linton, O. & Wang, H., 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Cambridge Working Papers in Economics 2218, Faculty of Economics, University of Cambridge.

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