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Estimation of Covariance Matrix with ARMA Structure Through Quadratic Loss Function

In: Contemporary Experimental Design, Multivariate Analysis and Data Mining

Author

Listed:
  • Defei Zhang

    (Honghe University, Department of Mathematics)

  • Xiangzhao Cui

    (Honghe University, Department of Mathematics)

  • Chun Li

    (Honghe University, Department of Mathematics)

  • Jianxin Pan

    (University of Manchester, Department of Mathematics)

Abstract

In this paper we propose a novel method to estimate the high-dimensional covariance matrix with an order-1 autoregressive moving average process, i.e. ARMA(1,1), through quadratic loss function. The ARMA(1,1) structure is a commonly used covariance structures in time series and multivariate analysis but involves unknown parameters including the variance and two correlation coefficients. We propose to use the quadratic loss function to measure the discrepancy between a given covariance matrix, such as the sample covariance matrix, and the underlying covariance matrix with ARMA(1,1) structure, so that the parameter estimates can be obtained by minimizing the discrepancy. Simulation studies and real data analysis show that the proposed method works well in estimating the covariance matrix with ARMA(1,1) structure even if the dimension is very high.

Suggested Citation

  • Defei Zhang & Xiangzhao Cui & Chun Li & Jianxin Pan, 2020. "Estimation of Covariance Matrix with ARMA Structure Through Quadratic Loss Function," Springer Books, in: Jianqing Fan & Jianxin Pan (ed.), Contemporary Experimental Design, Multivariate Analysis and Data Mining, chapter 0, pages 227-239, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46161-4_15
    DOI: 10.1007/978-3-030-46161-4_15
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