This paper theoretically and empirically analyzes backtesting portfolio VaR with estimation risk in an intrinsically multivariate framework. For the first time in the literature, it takes into account the estimation of portfolio weights in forecasting portfolio VaR and its impact on backtesting. It shows that the estimation risk from estimating the portfolio weights as well as that from estimating the multivariate dynamic model of asset returns make the existing methods in a univariate framework inapplicable. And it proposes a general theory to quantify estimation risk applicable to the present problem and suggests practitioners a simple but effective way to carry out valid inference to overcome the effect of estimation risk in backtesting portfolio VaR. A simulation exercise illustrates our theoretical findings. In application, a portfolio of three stocks is considered.

中文翻译：

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用估计的投资组合权重回测投资组合的风险价值

本文从理论上和实证上分析了具有内在多元框架中估计风险的回测投资组合 VaR。在文献中，它首次在预测投资组合 VaR 时考虑了投资组合权重的估计及其对回测的影响。这表明，估计投资组合权重的估计风险以及估计资产收益的多元动态模型的估计风险使得单变量框架中的现有方法不适用。并提出了适用于当前问题的量化估计风险的一般理论，并为从业者提供了一种简单而有效的方法来进行有效推理，以克服回测投资组合 VaR 中估计风险的影响。模拟练习说明了我们的理论发现。在应用中，