This paper is concerned with the statistical modeling of the latent dependence and comovement structures of multivariate financial data using a new approach based on mixed factorial hidden Markov models, and their applications in Value-at-Risk (VaR) valuation. This approach combines hidden Markov Models (HMM) with mixed latent factor models. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a mixture of factor analyzers observation process. This new switching specification provides an alternative, compact, model to handle intra-frame correlation and unobserved heterogeneity in financial data. For maximum likelihood estimation we have proposed an iterative approach based on the Expectation-Maximisation (EM) algorithm. Using a set of historical data, from the Tunisian foreign exchange market, the model parameters are estimated. Then, the fitted model combined with a modified Monte-Carlo simulation algorithm was used to predict the VaR of the Tunisian public debt portfolio. Through a backtesting procedure, we found that this new specification exhibits a good fit to the data, improves the accuracy of VaR predictions and can avoid serious violations when a financial crisis occurs.

中文翻译：

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混合因子隐马尔可夫模型预测投资组合风险价值

本文涉及使用基于混合因子隐马尔可夫模型的新方法对多元财务数据的潜在依赖关系和联动结构进行统计建模，及其在风险价值（VaR）评估中的应用。这种方法将隐马尔可夫模型（HMM）与混合潜在因子模型结合在一起。HMM生成分段的恒定状态演化过程，并且通过混合使用因子分析仪观察过程从状态向量中产生观察结果。这个新的交换规范提供了一个替代的，紧凑的模型来处理帧内关联和金融数据中未观察到的异质性。对于最大似然估计，我们已经提出了一种基于期望最大化（EM）算法的迭代方法。使用一组历史数据，从突尼斯外汇市场估计模型参数。然后，将拟合模型与改进的蒙特卡洛模拟算法结合使用来预测突尼斯公共债务投资组合的VaR。通过回测程序，我们发现此新规范与数据非常吻合，提高了VaR预测的准确性，并且可以避免发生金融危机时的严重违规行为。