我国股票市场高频数据波动率的预测研究

发布时间：2018-03-03 06:36

本文选题：高频数据　切入点：已实现波动率　出处：《大连理工大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文主要研究了我国股票市场高频金融数据的波动率的预测问题。首先,本文介绍了高频金融数据,它是相对于以前的以每年、每月、每周等为频率采集到的低频金融数据而言的,通常指以每天、每小时、每分钟甚至以每秒为频率所采集到的按时间先后顺序排列起来的金融数据序列。本文研究的数据样本采用了上证综指2010年1月4日到2012年6月29日的每1分钟的高频数据。其次,本文利用己实现波动率来估计实际波动率,从理论上给出了已实现波动率的计算方法,并且给出了已实现波动率的极限性质,这是本文进行研究的主要理论基础。接下来本文提到了时间序列的一个重要性质——长记忆性,并从时域和谱密度这两个角度给出了3个关于长记忆性的定义,并且着重介绍了长记忆性的一种检验方法——R/S检验法。然后,本文提到了ARFIMA(p, d, q)模型,提出了进行分数阶差分的意义,并且通过利用Stirling公式给出了一种做分数阶差分的简单方法,通过简单的R语言程序即可实现。最后,本文通过对上述高频金融数据的实证研究,对日对数己实现波动率(lnRV)的时间序列建立了ARFIMA(1,0.22,2)模型,并对其进行了向后10步的预测,由预测结果可以知道本文所建立的模型是合适的。最后又通过分数阶差分和1阶差分建模结果的比较可以知道本文提出的这种做分数阶差分的方法是有效且有意义的。
[Abstract]:This paper mainly studies the volatility prediction of high-frequency financial data in China's stock market. First, this paper introduces high-frequency financial data, which is compared with the previous annual, monthly, For low-frequency financial data collected at a frequency per week, usually in the form of a daily, an hour, A series of financial data in chronological order, even at frequencies per second, per minute. The data sample in this paper uses the high frequency data of every minute from January 4th 2010 to June 29th 2012 in the Shanghai Composite Index. Secondly, this paper estimates the actual volatility by using the realized volatility, gives the calculation method of the realized volatility theoretically, and gives the limit properties of the realized volatility. This is the main theoretical basis of this paper. In the next part of this paper, an important property of time series, long memory, is mentioned, and three definitions of long memory are given from the perspectives of time domain and spectral density. Then, the ARFIMAP, D, Q) model is mentioned, and the significance of fractional difference is put forward, and a simple method to do fractional order difference is given by using Stirling formula. Through a simple R language program can be achieved. Finally, based on the empirical study of the high frequency financial data mentioned above, this paper establishes the ARFIMA1 / 0.22 ~ 2) model for the time series of daily logarithmic self-realized volatility (LRV), and forecasts the model by 10 steps backward. From the prediction results, we can know that the model established in this paper is suitable. Finally, by comparing the results of fractional difference and first-order difference, we can see that the method proposed in this paper is effective and meaningful.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F832.51

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