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.,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.,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.

中文翻译：

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使用CAW型模型预测协方差矩阵的经济价值

本文的目的是双重的：改进传统的条件自回归Wishart（CAW）模型和异构自回归（HAR）-CAW模型，以解决异构杠杆效应并调整高频波动率。二是确定具有统计优势的CAW模型是否具有经济优势。基于高频数据，本研究根据异质市场假说提出了一种描述波动过程的新模型。因此，作者获得了必要且可靠的高频数据。通过设计两个均值方差框架并考虑了几种经济绩效指标，作者发现与基于日常数据的其他五个模型相比，CAW类型的模型，尤其是LHAR- CAW和HAR-CAW确实产生了可观的经济价值，