Estimation of covariance matrix with ARMA structure through quadratic loss function

Defei Zhang, Xiangzhao Cui, Chun Li, Jianxin Pan

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.
Original languageEnglish
Title of host publicationContemporary Experimental Design, Multivariate Analysis and Data Mining
EditorsJianqing Fan, Jianxin Pan
Place of PublicationSwitzerland
PublisherSpringer Nature
ISBN (Electronic)978-3-030-46161-4
ISBN (Print)978-3-030-46160-7
Publication statusPublished - 2020


  • ARMA (1,1) structure
  • covariance matrix
  • quadratic loss function


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