基于HMM-DNGARCH-X模型的股价预测研究  

Stock Price Forecasting Research Based on HMM-DNGARCH-X Model

作　　者：李月国 李贺宇 

机构地区：[1]长春工业大学数学与统计学院,吉林 长春

出　　处：《应用数学进展》2024年第11期4761-4771,共11页Advances in Applied Mathematics

摘　　要：股票预测对于投资者和金融市场具有重要意义,而同时刻画股票数据蕴含的非线性、非对称特性并解释外部冲击和复杂动态及状态变化的影响,对于传统GARCH模型来说存在局限性。因此为解决上述问题,本文结合非线性势GARCH (NPGARCH)和隐马尔可夫(HMM)两模型优势构建基于隐马尔可夫的带有外生变量的双非GARCH (HMM-DNGARCH-X)模型对股票收益率进行预测。首先根据HMM将股票价格波动划分为正常、异常状态,通过Baum-Welch算法估计模型参数,并采用Viterbi算法对隐状态序列进行识别;随后,将不同状态对应的收益率带入到HMM-DNGARCH-X模型进行预测分析。通过模拟研究,对模型的有效性进行了验证。基于上证国债指数的实证分析结果表明,与NPGARCH、GJR-GARCH、DNGARCH等模型相比HMM-DNGARCH-X模型的拟合损失均较小,并且预测效果显著优于其他模型。因此,所述HMM-DNGARCH-X模型能够较好地预测股票价格波动情况,在金融投资事件中具有广泛的应用潜力。Stock prediction is vital for investors and financial markets. Traditional GARCH models have limitations in capturing nonlinearity, asymmetry, and external shocks. To address this, we developed the HMM-DNGARCH-X model by combining the strengths of both models. Initially, HMM classifies stock price movements into normal and abnormal states, estimates parameters with the Baum-Welch algorithm, and identifies hidden states using the Viterbi algorithm. Returns from different states are then input into the HMM-DNGARCH-X model for prediction. Simulations validate the model’s effectiveness. Empirical analysis on the Shanghai Treasury Bond Index shows that HMM-DNGARCH-X has lower fitting losses and better predictive performance than NPGARCH, GJR-GARCH, and DNGARCH models. Thus, HMM-DNGARCH-X demonstrates significant potential for predicting stock price volatility in financial investments.

关 键 词：对数收益率 隐马尔可夫模型 HMM-DNGARCH-X模型 非线性 非对称性 

分 类 号：F83[经济管理—金融学]