MS-DFM模型的参数估计及其在股市周期识别中的应用  

Parameter estimation of MS-DFM model and its application in stock market cycle recognition

作　　者：杨柳[1] 刘鑫[1] 马维军[1] 袁超凤 YANG Liu;LIU Xin;MA Weijun;YUAN Chaofeng(School of Mathematics and Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学与科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2024年第4期406-416,共11页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省省属高校基本科研业务费项目(2022-KYYWF-1100,YWK10236200144)。

摘　　要：对已有的马尔科夫转移动态因子模型提出了一个新的参数估计方法——两步最大期望(Expectation-maximization,EM)法,通过对马尔科夫转移动态因子模型进行重新参数化,将其转换为混合动态因子模型,并将因子与状态均视为潜变量,利用EM算法实现对重新参数化后的参数以及因子得分的估计。将因子得分视为已知数据、状态视为潜变量,针对每个因子序列建立马尔科夫转移自回归模型,利用EM算法对依状态变化的截距项和自回归系数进行估计,并对状态与拐点进行识别。通过数值模拟验证该方法的有效性,并将该模型与估计方法用于我国沪深股市股票数据分析中,对股市行业周期进行度量和识别。A novel parameter estimation method,the two-step expectation-maximization(EM)approach,is presented for existing Markov switching dynamic factor models.The Markov switching dynamic factor models are re-parameterized to transform them into a mixed dynamic factor model,with both factors and states treated as latent variables,the EM algorithm is employed to estimate the parameters and factor scores in the re-parameterized model.With factor scores taken as known data and states as latent variables,Markov switching auto-regressive models are established for each factor sequence.The EM algorithm is utilized to estimate the intercept terms and auto-regressive coefficients that vary with states,and to identify states and turning points.The effectiveness of this method is verified through numerical simulations.The model and estimation methods are applied to analyze a stock market data set from the Shanghai and Shenzheng stock exchanges in China,aiming to measure and identify industry cycles in the stock market.

关 键 词：马尔科夫转移模型 动态因子模型 马尔科夫转移动态因子模型 EM算法 

分 类 号：O212[理学—概率论与数理统计]