本文为加拿大西蒙菲莎大学（作者：Yingjian Zhang）的硕士论文，共102页。

在本文中，我们对隐马尔可夫模型（HMM）进行了扩展，解决了金融时间序列模型的两个最重要挑战：非平稳和非线性。具体地说，我们将HMM扩展到包含一个新的指数加权期望最大化（EM）算法来处理这两个挑战。研究结果表明，该扩展算法不仅可以对序列数据进行建模，而且可以对动态的财务时间序列进行建模。我们证明了HMM参数的更新规则可以用模型变量的指数滑动平均值的形式编写，这样我们就可以利用现有的分析技术。

我们进一步提出了一种能自动调整训练灵敏度的双加权EM算法，并利用EM定理的方法证明了算法的收敛性。实验结果表明，我们的模型在1994年至2002年的5个400天测试期内持续超过标准普尔500指数，包括牛市和熊市。在夏普比率方面，我们的模型也始终优于标准普尔500共同基金的前5名。

In this thesis, we develop an extension of the Hidden Markov Model (HMM) that addresses two of the most important challenges of financial time series modeling: non-stationary and non-linearity. Specifically, we extend the HMM to include a novel exponentially weighted Expectation-Maximization (EM) algorithm to handle these two challenges. We show that this extension allows the HMM algorithm to model not only sequence data but also dynamic financial time series. We show the update rules for the HMM parameters can be written in a form of exponential moving averages of the model variables so that we can take the advantage of existing technical analysis techniques. We further propose a double weighted EM algorithm that is able to adjust training sensitivity automatically. Convergence results for the proposed algorithms are proved using techniques from the EM Theorem. Experimental results show that our models consistently beat the S&P 500 Index over five 400-day testing periods from 1994 to 2002, including both bull and bear markets. Our models also consistently outperform the top 5 S&P 500 mutual funds in terms of the Sharpe Ratio.

1 引言

2 隐马尔科夫模型

3 基于HMM的金融时间序列分析

4 基于HMM的指数加权EM算法

5 实验结果

6 结论与未来研究展望

附录A 术语列表 

下载英文原文地址：

http://page2.dfpan.com/fs/alcdj22214297164554/  

更多精彩文章请关注微信号：