马尔可夫机制转换模型的统计分析及金融方面的应用研究

发布时间：2018-06-28 14:48

本文选题：上证指数 + 汇率　；参考：《浙江理工大学》2017年硕士论文

【摘要】：马尔可夫机制转换模型是当今比较流行的一种动态时间序列模型,它能将不完全可预见的、不确定的机制转换看作为一个随机变量,在时间上就具备了随机性和连续性的特点。随着马尔可夫机制转换模型的不断发展,将其与和传统的时间序列模型相结合,被广泛的应用于经济和金融领域的研究中。在大量的实证研究中发现,金融时间序列具有波动聚集性、结构不稳定性和尖峰后尾的特点,而传统的时间序列已经不能很好的刻画金融时间序列的这些特性。为更好地解决这类问题,将马尔可夫机制转换模型与传统的时间序列模型结合起来,提出了-和-等模型,解决了结构突变所带来的问题。但由于残差序列服从不同的分布,所以在正态分布的基础上,拓展到分布和广义误差分布等有偏分布中,大大提高了模型的拟合效果。本文选取2005年1月4日到2016年9月29日上证指数和2009年11月2日至2016年9月29号汇率日收盘价的对数收益率序列作为研究样本。分别采用基于估计方法下的模型和基于估计方法不同分布形式的-模型对数据进行建模,并对模型参数进行比较分析。在此基础上,运用不同分布形式下的-模型对样本外数据进行预测,并对预测结果进行比较分析。同时,应用高斯混合模型的算法对数据的状态数目进行检验。实证结果表明:(1)运用估计方法对模型的参数进行估计,通过构造系数的方法进行实证分析,并与基于估计方法下的-模型的参数进行比较分析,发现--模型能够更好的对数据进行描述。(2)在数据的持续性研究中,采用基于估计方法下的不同分布形式的-模型,对数据进行样本外预测,分布下的预测值更贴近于真实值,在拟合程度和波动性描述上效果更好。(3)利用高斯混合模型的算法,对两状态的-模型进假设性检验,通过对数似然估计值大小的比较,认为股票与汇率市场分两状态进行分析比较好。
[Abstract]:Markov mechanism transformation model is a popular dynamic time series model. It can treat the incomplete predictable and uncertain mechanism transformation as a random variable, which has the characteristics of randomness and continuity in time. With the development of Markov mechanism transformation model, it is combined with the traditional time series model and is widely used in the field of economics and finance. In a large number of empirical studies, it is found that financial time series have the characteristics of volatility aggregation, structural instability and peak tail, but the traditional time series can not well describe these characteristics of financial time series. In order to solve this kind of problem better, the Markov mechanism transformation model is combined with the traditional time series model, and the-sum-model is proposed, which solves the problem caused by the structural mutation. But because the residuals are distributed from different distribution, based on the normal distribution, it is extended to the biased distribution and generalized error distribution, which greatly improves the fitting effect of the model. This paper selects the logarithmic yield series of the Shanghai Stock Exchange Index from January 4, 2005 to September 29, 2016 and the exchange rate daily closing price from November 2, 2009 to September 29, 2016 as research samples. The model based on estimation method and the model based on different distribution forms of estimation method are used to model the data, and the parameters of the model are compared and analyzed. On this basis, the data outside the sample are predicted by using the-model with different distribution forms, and the prediction results are compared and analyzed. At the same time, the algorithm of Gao Si hybrid model is used to test the number of data states. The empirical results show that: (1) the estimation method is used to estimate the parameters of the model, the empirical analysis is carried out by the method of constructing coefficient, and the parameters of the model based on the estimation method are compared with those of the model. Discovery-model can better describe the data. (2) in the research of data persistence, using the different distribution model based on estimation method, the data is predicted outside the sample, and the predicted value under the distribution is closer to the real value. It is more effective in describing the degree of fit and volatility. (3) by using the algorithm of Gao Si mixed model, we test the hypothesis of the two-state model and compare the magnitude of the logarithmic likelihood estimation. It is better to analyze the stock and exchange rate market in two states.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F832;O211.61

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