Statistics and Its Interface

Volume 13 (2020)

Number 1

Modeling RCOV matrices with a generalized threshold conditional autoregressive Wishart model

Pages: 77 – 89



Yan Cui (School of Mathematics, Jilin University, Changchun, China)

Fukang Zhu (School of Mathematics, Jilin University, Changchun, China)

Wai Keung Li (Department of Mathematics and Information Technology, Education University of Hong Kong)


In this article, we propose a generalized threshold conditional autoregressive Wishart (GTCAW) model to analyze the dynamics of the realized covariance (RCOV) matrices. This model extends the idea of [29] to a threshold framework. It is believed that, as in many financial time series, the dynamic of RCOV matrices exhibits nonlinearity and may be better explained by a threshold type model. The noncentrality matrix and scale matrix of the Wishart distribution are piecewise linear driven by the lagged values of RCOV matrices and retain two different sources of dynamics. The GTCAW model guarantees the symmetry and positive definiteness of RCOV matrices, some simulation results on the maximum likelihood estimation are also given. Real data examples based on daily RCOV matrices present the nonlinear behavior in these time series and the usefulness of the proposed model.


GTCAW, RCOV matrices, Threshold, Volatility, Wishart.

2010 Mathematics Subject Classification

Primary 91B84. Secondary 62M10.

Li’s work is supported partially by the Hong Kong General Research Fund grant 17303315.

Zhu’s work is supported by National Natural Science Foundation of China (Nos. 11871027, 11731015), Science and Technology Developing Plan of Jilin Province (No. 20170101057JC), and Cultivation Plan for Excellent Young Scholar Candidates of Jilin University.

Received 30 August 2018

Accepted 23 August 2019

Published 7 November 2019