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A segmented regime-switching model with its application to stock market indices

机译：分段政权转换模型及其在股市指数中的应用

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Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui,China;Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada;Manulife Financial Inc., Toronto, Ontario, Canada;Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui,China;%This paper evaluates the ability of a Markov regime-switching log-normal (RSLN) model to capture the time-varying features of stock return and volatility. The model displays a better ability to depict a fat tail distribution as compared with using a log-normal model, which means that the RSLN model can describe observed market behavior better. Our major objective is to explore the capability of the model to capture stock market behavior over time. By analyzing the behavior of calibrated regime-switching parameters over different lengths of time intervals, the change-point concept is introduced and an algorithm is proposed for identifying the change-points in the series corresponding to the times when there are changes in parameter estimates. This algorithm for identifying change-points is tested on the Standard and Poor's 500 monthly index data from 1971 to 2008, and the Nikkei 225 monthly index data from 1984 to 2008. It is evident that the change-points we identify match the big events observed in the US stock market and the Japan stock market (e.g., the October 1987 stock market crash), and that the segmentations of stock index series, which are defined as the periods between change-points, match the observed bear-bull market phases.
机译：中国科学技术大学统计与金融系，安徽合肥；加拿大约克大学约克大学数学与统计系；加拿大安大略省；加拿大安大略省多伦多宏利金融公司；统计与统计系中国科学技术大学金融学院，安徽合肥；％本文评估了马尔可夫政权转换对数正态（RSLN）模型捕获股票收益率和波动率的时变特征的能力。与使用对数正态模型相比，该模型显示出更好的描绘肥尾分布的能力，这意味着RSLN模型可以更好地描述观察到的市场行为。我们的主要目标是探索该模型捕捉一段时间内股票市场行为的能力。通过分析在不同时间间隔长度上校准的状态切换参数的行为，引入了变化点概念，并提出了一种算法，用于识别与参数估计值发生变化的时间相对应的序列中的变化点。 1971年至2008年的标准普尔500指数月度数据和1984年至2008年的Nikkei 225指数月度数据均采用了这种识别变化点的算法。很明显，我们确定的变化点与观察到的大事件相匹配。在美国股票市场和日本股票市场（例如1987年10月的股票市场崩盘）中，股票指数系列的细分（定义为变化点之间的时间段）与观察到的熊市市场阶段相匹配。

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