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The economic value of using CAW-type models to forecast covariance matrix

Shuran Zhao (Ocean University of China, Qingdao, China) (Humanities and Social Science Key Research Base of Ministry of Education – Institute of Marine Development, Ocean University of China, Qingdao, China)
Jinchen Li (Ocean University of China, Qingdao, China)
Yaping Jiang (Ocean University of China, Qingdao, China)
Peimin Ren (Qingdao University, Qingdao, China)

China Finance Review International

ISSN: 2044-1398

Article publication date: 16 August 2019

Issue publication date: 16 August 2019




The purpose of this paper is twofold: to improve the traditional conditional autoregressive Wishart (CAW) and heterogeneous autoregressive (HAR)-CAW model to account for heterogeneous leverage effect and to adjust the high-frequency volatility. The other is to confirm whether CAW-type models that have statistical advantages have economic advantages.


Based on the high-frequency data, this study proposed a new model to describe the volatility process according to the heterogeneous market hypothesis. Thus, the authors acquire needed and credible high-frequency data.


By designing two mean-variance frameworks and considering several economic performance measures, the authors find that compared with five other models based on daily data, CAW-type models, especially LHAR-CAW and HAR-CAW, indeed generate the substantial economic values, and matrix adjustment method significantly improves the three CAW-type performances.

Research limitations/implications

The findings in this study suggest that from the aspect of economics, LHAR-CAW model can more accurately built the dynamic process of return rates and covariance matrix, respectively, and the matrix adjustment can reduce bias of realized volatility as covariance matrix estimator of return rates, and greatly improves the performance of unadjusted CAW-type models.

Practical implications

Compared with traditional low-frequency models, investors should allocate assets according to the LHAR-CAW model so as to get more economic values.


This study proposes LHAR-CAW model with the matrix adjustment, to account for heterogeneous leverage effect and empirically show their economic advantage. The new model and the new bias adjustment approach are pioneering and promote the evolution of financial econometrics based on high-frequency data.



The paper was sponsored by Humanities and Social Science Youth Fund Projects of Ministry of Education (18YJA790113), the National Natural Science Foundation of Shandong (ZR2017MG005), Major projects of the National Social Science Fund(15ZDB171).


Zhao, S., Li, J., Jiang, Y. and Ren, P. (2019), "The economic value of using CAW-type models to forecast covariance matrix", China Finance Review International, Vol. 9 No. 3, pp. 338-359.



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