Statistics and Its Interface
Volume 13 (2020)
Modeling RCOV matrices with a generalized threshold conditional autoregressive Wishart model
Pages: 77 – 89
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  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