股票量价渐近分布及其变点的统计过程控制监测
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摘要
本论文由两部分组成。
第一部分研究证券市场中成交量和收益率之间的关系。证券市场上有一句名言:“价走量先行”,说明了证券价格与成交量有一种必然的联系。
国内外大量的学者对量价关系从理论和实证角度进行了广泛的研究。理论模型,比如“混合分布假设”模型、“信息顺序到达模型”和“噪声交易理性预期均衡模型”等,都认为量和价有共同确定的关系。
受这些模型的影响,有许多实证分析的文献寻求交易量与价格波动之间具有即期正相关的证据。大多数模型使用间接的关系来解释量价关系,因而,改变了原始序列。至于成交量如何影响这些统计特性,则仍无法解释清楚。
第二章以“量是股价上涨的原动力,而股价又反作用于量,两者相互作用”这一经典论断为背景,考虑到股票价格的变动不仅受它本身的量、价历史数据的影响,而且还会受到其他股票的量价波动的影响,我们提出了一类直接反映量价关系的非线性统计模型。通过分析收益率、成交量的相对变化率及它的残差,我们研究了收益率序列的渐近分布。
第三章应用近代时间序列分析的方法,从平稳性检验、异方差检验、长记忆性检验等方面对沪市综合指数进行实证分析,揭示了中国证券市场的基本特征,为寻求合理的金融预测模型奠定了基础。针对在第二章提出的模型,我们做了实证分析。得到了考虑成交量时股价的要比瞎猜要好的结论。
第四章和第五章为一部分,主要研究用统计控制过程理论监测均值位移。
第四章我们研究了利用若干个具有不同参考值δ的控制图构造一个相应的多图(Multi-Chart),证明了多图的平均链长(ARL)小于构成它的控制图的平均链长的均值;证明了CUSUM-多图的渐近最优性。
对均值位移已知情形,证明了CUSUM-多图能够很快达到其最优下界,
对均值位移未知情形,证明了最优设计应满足的表达式,并证明CUSUM-多图比任何单个的CUSUM控制图的性能都好。
通过Monte Carlo模拟,进一步证实了CUSUM-多图有能快速监测均值位移的范围、对各种情形的设计简单灵活、极大地减少了计算的复杂性等优点,并且在整体上比CUSUM控制图、EWMA控制图和EWMA-多图更有效、更稳健。
第五章我们应用CUSUM控制图对沪市综合指数在不同阶段的序列的均值位移进行监测,给出了一种基于考虑成交量的控制图的设计。通过CUSUM控制图超出上临界值或下临界值,结合此时的成交率(累积成交率)的大小,我们给出一种判别股票买卖时机的准则。将监测到均值位移时的值与下一时刻股票收益率进行比较,我们的模型预测效果满意。
This dissertation is composed of two parts.
In the first part, we investigate the relationship between the stock price and tradingvolume of stock market . There is a logion in the stock market that”It takes volumeto price move”, it show that there is certainly relationship between the stock price andtrading volume. There is an extensive research into the theoretical and empirical aspectsof the stock price and trading volume relationship. Theoretical models, such as the”MDH”(mixture of distribution hypothesis) model,”SIF”(the sequential information?ow) model and framework in Noisy rational expectation equilibrium bivariate model, andso on, suggest that volume and price are jointly determined. Relying on the motivationof these models, most of the empirical literatures test and consistently find evidence for apositive contemporaneous correlation between volume and the price variability. Most ofthese models use indirect variable to explain the price-volume relationship, and therefore,the original data are fully changed in these models. It is di?cult to explain how thevolume e?ect this Statistical characteristic.
In the second chapter, we propose a general non-linear statistical model, by the factthat a stock’s price can be e?ected not only by itself historical volumes and prices, butalso by the other stocks’volumes and prices. Then, we study the asymptotic distributionof a sequence of the return by analyzing the relationship between the return, relative rateof trading volume and its residues.
In the chapter 3, we use the newly method of time series analysis to test the shanghai’sstock index by the hypothesis tests based on stationarity, heteroskedasticity ,long memory,and so on. For the model put forwards in the chapter two, we make empirical analysis,and obtain some forecast results of shock price better than the guess result considering oftrading volume.
The chapter 4 and chapter 5 are the other part. We study Mainly using Statisticalprocess control (SPC) theory to detecting several known or unknown mean shifts.
In the chapter 4, we study a multi-chart basically consists of multiple control chartswith di?erent reference valuesδ, and prove the ARL of multi-chart is less than the averageARLs of its constituent charts, and prove the asymptotic optimality of the CUSUM Multi-chart.
For the case of known mean shifts, we prove CUSUM multi-chart can fast attain itsoptimality lower limit. For the case of unknown mean shifts, we find the expression of anoptimal design of the CUSUM multi-chart, and prove the CUSUM multi-chart has betterperformance than that of any single constituent CUSUM chart in detecting an unknownmean shift.
Further, By Monte Carlo simulating, make sure the CUSUM multi-chart with meritof the fast detecting a range of mean shifts, and design simply and ?exible, decreasecomputational complexity, and the CUSUM multi-chart is superior (rapid and robust)on the whole to the CUSUM, EWMA, EWMA multi-chart, and GLR chart in detectingvarious mean shifts.
In the chapter 5, by CUSUM chart, we detect the mean shifts of series of shanghai’sstock return in several stages, give out a design of CUSUM chart based on considering of trading volume. BY CUSUM chart exceeding upper control limit or lower control limit,combining contemporaneous the rate of trading volume, we give a rule of judgement whenthe stock will buy or sale. we compare the value of detecting mean shifts with the returnof stock at the next time, and think that our model for forecasting is relatively satisfied.
第一部分研究证券市场中成交量和收益率之间的关系。证券市场上有一句名言:“价走量先行”,说明了证券价格与成交量有一种必然的联系。
国内外大量的学者对量价关系从理论和实证角度进行了广泛的研究。理论模型,比如“混合分布假设”模型、“信息顺序到达模型”和“噪声交易理性预期均衡模型”等,都认为量和价有共同确定的关系。
受这些模型的影响,有许多实证分析的文献寻求交易量与价格波动之间具有即期正相关的证据。大多数模型使用间接的关系来解释量价关系,因而,改变了原始序列。至于成交量如何影响这些统计特性,则仍无法解释清楚。
第二章以“量是股价上涨的原动力,而股价又反作用于量,两者相互作用”这一经典论断为背景,考虑到股票价格的变动不仅受它本身的量、价历史数据的影响,而且还会受到其他股票的量价波动的影响,我们提出了一类直接反映量价关系的非线性统计模型。通过分析收益率、成交量的相对变化率及它的残差,我们研究了收益率序列的渐近分布。
第三章应用近代时间序列分析的方法,从平稳性检验、异方差检验、长记忆性检验等方面对沪市综合指数进行实证分析,揭示了中国证券市场的基本特征,为寻求合理的金融预测模型奠定了基础。针对在第二章提出的模型,我们做了实证分析。得到了考虑成交量时股价的要比瞎猜要好的结论。
第四章和第五章为一部分,主要研究用统计控制过程理论监测均值位移。
第四章我们研究了利用若干个具有不同参考值δ的控制图构造一个相应的多图(Multi-Chart),证明了多图的平均链长(ARL)小于构成它的控制图的平均链长的均值;证明了CUSUM-多图的渐近最优性。
对均值位移已知情形,证明了CUSUM-多图能够很快达到其最优下界,
对均值位移未知情形,证明了最优设计应满足的表达式,并证明CUSUM-多图比任何单个的CUSUM控制图的性能都好。
通过Monte Carlo模拟,进一步证实了CUSUM-多图有能快速监测均值位移的范围、对各种情形的设计简单灵活、极大地减少了计算的复杂性等优点,并且在整体上比CUSUM控制图、EWMA控制图和EWMA-多图更有效、更稳健。
第五章我们应用CUSUM控制图对沪市综合指数在不同阶段的序列的均值位移进行监测,给出了一种基于考虑成交量的控制图的设计。通过CUSUM控制图超出上临界值或下临界值,结合此时的成交率(累积成交率)的大小,我们给出一种判别股票买卖时机的准则。将监测到均值位移时的值与下一时刻股票收益率进行比较,我们的模型预测效果满意。
This dissertation is composed of two parts.
In the first part, we investigate the relationship between the stock price and tradingvolume of stock market . There is a logion in the stock market that”It takes volumeto price move”, it show that there is certainly relationship between the stock price andtrading volume. There is an extensive research into the theoretical and empirical aspectsof the stock price and trading volume relationship. Theoretical models, such as the”MDH”(mixture of distribution hypothesis) model,”SIF”(the sequential information?ow) model and framework in Noisy rational expectation equilibrium bivariate model, andso on, suggest that volume and price are jointly determined. Relying on the motivationof these models, most of the empirical literatures test and consistently find evidence for apositive contemporaneous correlation between volume and the price variability. Most ofthese models use indirect variable to explain the price-volume relationship, and therefore,the original data are fully changed in these models. It is di?cult to explain how thevolume e?ect this Statistical characteristic.
In the second chapter, we propose a general non-linear statistical model, by the factthat a stock’s price can be e?ected not only by itself historical volumes and prices, butalso by the other stocks’volumes and prices. Then, we study the asymptotic distributionof a sequence of the return by analyzing the relationship between the return, relative rateof trading volume and its residues.
In the chapter 3, we use the newly method of time series analysis to test the shanghai’sstock index by the hypothesis tests based on stationarity, heteroskedasticity ,long memory,and so on. For the model put forwards in the chapter two, we make empirical analysis,and obtain some forecast results of shock price better than the guess result considering oftrading volume.
The chapter 4 and chapter 5 are the other part. We study Mainly using Statisticalprocess control (SPC) theory to detecting several known or unknown mean shifts.
In the chapter 4, we study a multi-chart basically consists of multiple control chartswith di?erent reference valuesδ, and prove the ARL of multi-chart is less than the averageARLs of its constituent charts, and prove the asymptotic optimality of the CUSUM Multi-chart.
For the case of known mean shifts, we prove CUSUM multi-chart can fast attain itsoptimality lower limit. For the case of unknown mean shifts, we find the expression of anoptimal design of the CUSUM multi-chart, and prove the CUSUM multi-chart has betterperformance than that of any single constituent CUSUM chart in detecting an unknownmean shift.
Further, By Monte Carlo simulating, make sure the CUSUM multi-chart with meritof the fast detecting a range of mean shifts, and design simply and ?exible, decreasecomputational complexity, and the CUSUM multi-chart is superior (rapid and robust)on the whole to the CUSUM, EWMA, EWMA multi-chart, and GLR chart in detectingvarious mean shifts.
In the chapter 5, by CUSUM chart, we detect the mean shifts of series of shanghai’sstock return in several stages, give out a design of CUSUM chart based on considering of trading volume. BY CUSUM chart exceeding upper control limit or lower control limit,combining contemporaneous the rate of trading volume, we give a rule of judgement whenthe stock will buy or sale. we compare the value of detecting mean shifts with the returnof stock at the next time, and think that our model for forecasting is relatively satisfied.
引文
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