基于高频数据的金融市场分析
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摘要
近年来,对金融高频数据研究已经成为了金融计量学的一个全新的研究领域和方向。本论文主要研究了金融市场高频数据的特性、建模以及应用问题。本文的主要工作和创新点如下:
1)分别基于已实现波动和已实现极差波动与积分波动之间误差项的渐近分布,给出了一个高频数据抽样方法。
2)基于RV-VAR类波动模型,从单位根的角度给出了关于条件方差的持续性、协同持续的定义,证明了波动非持续性、协方差平稳和波动方程特征根在单位圆内具有内在的一致性。同时,也证明了上述给出的协同持续定义与Bollerslev和Engle提出的协同持续概念具有内在的一致性。扩展线性协同持续定义到非线性情况,给出了非线性协同持续的定义,证明了了它们之间的内在关系。
3)基于RV-VAR模型,应用Bollerslev和Engle提出的持续和协同持续概念,证明了RV-VAR模型存在线性协同持续的充要条件和寻找这种线性协同持续向量的方法,又基于小波神经网络理论建立非线性协同持续模型。通过实证分析,表明沪深两股市之间不存在线性协同持续关系,但存在非线性协同持续关系。
4)在RV-ARMA模型基础上,从条件方差持续性的角度,讨论了条件方差的持续性对资产资本定价模型的影响。又进一步讨论了多资产组合条件下,RV-VAR模型持续性对组合投资的影响。对高阶矩进行建模,并给出了时变条件四阶矩的资产定价模型。给出了基于RV-ARMA模型和GARCH模型的实证分析,指出当模型具有单位根时条件方差对资产定价的影响是持续的,并对持续性进行了比较。
5)分别从模拟试验和理论上,比较了已实现波动和已实现极差波动两种度量方法。给出了考虑“日历效应”的加权已实现极差波动,并说明了已实现极差波动只是加权已实现极差波动的特例。通过一系列实证分析,也说明了加权已实现极差波动是更有效的波动估计量。
In recent years, research on high frequency data has been a new research field and direction in financial econometrics. The paper studies the characharistic,modeling and application of high frequency data.The key points and main achievements are listed as follows:
1)An optimal sampling method is given based on asymptotic distribution of error term between RV(realized volatility),RRV(realized range-based volatility) and IV(integrated volatility),respectively.
2)The fact that volatility non-persistence,covariance stationarity and characteristic root lying inside the unit circle of volatility equation have inherent consistency is proved when the definitions of persistence,co-persistence on conditional variance are given from point of view of unit root based on RV-VAR (realized volatility-vector autoregression)family model.at the same time,the co-persistence definition given above which is inherent consistency with co-persistence concept of Bollerslev&Engle is also proved. The definition of linear co-persistence is expanded to non-liear case where non-liear co-persistence definition is given and inherent relationships between linear co-persistence and non-linear co-persistence are testified.
3)The existence of necessary and sufficient condition of linear co-persistence in RV-VAR model is proved and how to find this linear co-persistence vector is given.The model of non-linear co-persistence is also set up based on wavelet neural network theory.By empirical analysis ,it is clear that linear co-persistence does not exit between Shanghai stock market and Shenzhen stock market,but non-linear co-persistence exits between them.
4)Based on the RV-ARMA(realized volatility-autoregressive and moving average) model,it is discussed that the persistence of conditional variances has a effect on capital asset pricing model(CAPM) from persistence viewpoint. Moreover, we analyze the persistence of multi-asset portfolio which follows a RV-VAR process. By using high frequency data, modeling higher moments of volatility is given and the time-conditional CAPM is put forward.Based on the RV-ARMA and GARCH model, the empirical analysis points out the facts that the conditional variances have a persistent effect on capital asset pricing in model with root and their persistence is compared.
5)Two volatility estimator based on RV and RRV are compared from theory and simulated test,respectively.WRRV(weighted realized range-based volatility) is given based on the consideration of calendar effect and RRV is only special case of WRRV.it is pointed out that WRRV is more perfect volatility estimator.
1)分别基于已实现波动和已实现极差波动与积分波动之间误差项的渐近分布,给出了一个高频数据抽样方法。
2)基于RV-VAR类波动模型,从单位根的角度给出了关于条件方差的持续性、协同持续的定义,证明了波动非持续性、协方差平稳和波动方程特征根在单位圆内具有内在的一致性。同时,也证明了上述给出的协同持续定义与Bollerslev和Engle提出的协同持续概念具有内在的一致性。扩展线性协同持续定义到非线性情况,给出了非线性协同持续的定义,证明了了它们之间的内在关系。
3)基于RV-VAR模型,应用Bollerslev和Engle提出的持续和协同持续概念,证明了RV-VAR模型存在线性协同持续的充要条件和寻找这种线性协同持续向量的方法,又基于小波神经网络理论建立非线性协同持续模型。通过实证分析,表明沪深两股市之间不存在线性协同持续关系,但存在非线性协同持续关系。
4)在RV-ARMA模型基础上,从条件方差持续性的角度,讨论了条件方差的持续性对资产资本定价模型的影响。又进一步讨论了多资产组合条件下,RV-VAR模型持续性对组合投资的影响。对高阶矩进行建模,并给出了时变条件四阶矩的资产定价模型。给出了基于RV-ARMA模型和GARCH模型的实证分析,指出当模型具有单位根时条件方差对资产定价的影响是持续的,并对持续性进行了比较。
5)分别从模拟试验和理论上,比较了已实现波动和已实现极差波动两种度量方法。给出了考虑“日历效应”的加权已实现极差波动,并说明了已实现极差波动只是加权已实现极差波动的特例。通过一系列实证分析,也说明了加权已实现极差波动是更有效的波动估计量。
In recent years, research on high frequency data has been a new research field and direction in financial econometrics. The paper studies the characharistic,modeling and application of high frequency data.The key points and main achievements are listed as follows:
1)An optimal sampling method is given based on asymptotic distribution of error term between RV(realized volatility),RRV(realized range-based volatility) and IV(integrated volatility),respectively.
2)The fact that volatility non-persistence,covariance stationarity and characteristic root lying inside the unit circle of volatility equation have inherent consistency is proved when the definitions of persistence,co-persistence on conditional variance are given from point of view of unit root based on RV-VAR (realized volatility-vector autoregression)family model.at the same time,the co-persistence definition given above which is inherent consistency with co-persistence concept of Bollerslev&Engle is also proved. The definition of linear co-persistence is expanded to non-liear case where non-liear co-persistence definition is given and inherent relationships between linear co-persistence and non-linear co-persistence are testified.
3)The existence of necessary and sufficient condition of linear co-persistence in RV-VAR model is proved and how to find this linear co-persistence vector is given.The model of non-linear co-persistence is also set up based on wavelet neural network theory.By empirical analysis ,it is clear that linear co-persistence does not exit between Shanghai stock market and Shenzhen stock market,but non-linear co-persistence exits between them.
4)Based on the RV-ARMA(realized volatility-autoregressive and moving average) model,it is discussed that the persistence of conditional variances has a effect on capital asset pricing model(CAPM) from persistence viewpoint. Moreover, we analyze the persistence of multi-asset portfolio which follows a RV-VAR process. By using high frequency data, modeling higher moments of volatility is given and the time-conditional CAPM is put forward.Based on the RV-ARMA and GARCH model, the empirical analysis points out the facts that the conditional variances have a persistent effect on capital asset pricing in model with root and their persistence is compared.
5)Two volatility estimator based on RV and RRV are compared from theory and simulated test,respectively.WRRV(weighted realized range-based volatility) is given based on the consideration of calendar effect and RRV is only special case of WRRV.it is pointed out that WRRV is more perfect volatility estimator.
引文
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