已实现协方差的平滑转移多元异质自回归模型的研究
发布时间：2018-07-28 09:11
【摘要】：投资组合和风险管理的发展迫切要求投资组合理论的完善,而投资者规避风险的愿望要求构建能更加准确地预测市场当中的风险的模型。基于高频数据的多资产的已实现协方差阵作为组合风险水平的一个度量,其准确预测是一个引人关注的问题。目前,基于高频的已实现波动率模型的研究有很多,但是因为多变量模型的诸多限制,基于已实现协方差的多变量模型相对而言很少,主要有多变量的HAR模型、WAR模型等。波动的不对称性的问题之发现已久,其主要体现在过往利好和利空的冲击对未来波动的影响不同,利空信息相对利好信息对波动影响更大,此即杠杆效应。除此之外,波动还具有其他不对称性,例如大小不对称性。为了解释这一现象,已有诸多研究将平滑转移引入单变量波动率模型,过往研究证明平滑转移引入单变量的波动率模型不仅能提高模型的拟合程度,也能改进模型的预测性能。但是,目前将平滑转移引入多变量波动率模型的研究则严重不足,而基于已实现协方差阵的平滑转移模型实证研究则尚为空白领域。本文在由单变量HAR模型扩展到多元情况形式的MHAR模型当中引入平滑转移函数,并用2007至2016年上证50ETF的7只个股以及上证50指数作为数据,对个股的已实现协方差阵进行建模。因为协方差阵需要保证正定性,故一般做法是对协方差阵进行正定变换,用其变换后的拉直向量作为回归变量。但由于正定变换后,协方差阵各个元素的自相关性和不对称性并不统一而且受到很大影响,故本文提出两种方法:一种是提出MHAR-diag模型,将对角元素和非对角元素赋予不同的自回归系数,基于这种模型再引入平滑转移函数以刻画对角元素和非对角元素不对称性的不同;另一种方法是考虑非正定变换,本文提出一种非正定变换为lcor变换,并在建立模型时加以正定性限制条件建模。本文利用DM检验和MCS检验,利用多个损失函数综合对比各个模型的样本外预测能力。实证显示,不论是对经对数变换或lcor变换后的协方差阵建模,MHAR-diag模型相对于普通的MHAR模型在所有损失函数下能够改善模型的预测能力;同时,本文提出的lcor变换在同样的模型形式下比对数变换能得到更好的样本外预测效果;最后,在全模型的MCS检验当中,基于lcor变换的加入平滑转移的MHAR-splitST模型综合而言于正常波动阶段预测性能最优。
[Abstract]:The development of portfolio and risk management urgently requires the perfection of portfolio theory, and the desire of investors to avoid risks requires the establishment of a more accurate model to predict the risks in the market. The realized covariance matrix of multi-assets based on high-frequency data is a measure of portfolio risk level, and its accurate prediction is an interesting problem. At present, there are many researches on realized volatility models based on high frequency, but because of the limitations of multivariate models, there are few multivariate models based on realized covariance, such as multivariable HAR model and war model. The problem of asymmetry of volatility has been discovered for a long time, which is mainly reflected in the fact that the impact of positive and negative shocks on future volatility is different, and that the impact of good information on volatility is greater than that of good information, which is called leverage effect. In addition, fluctuations have other asymmetries, such as size asymmetry. In order to explain this phenomenon, many researches have introduced smooth transfer into univariate volatility model. Previous studies have proved that smooth transfer can not only improve the fitting degree of the model, but also improve the prediction performance of the model. However, the research of introducing smooth transfer into multivariate volatility model is seriously inadequate, but the empirical study of smooth transfer model based on realized covariance matrix is still a blank field. In this paper, the smooth transfer function is introduced in the MHAR model, which is extended from univariate HAR model to multivariate MHAR model, and the realized covariance matrix of individual stock is modeled by using 7 stocks of 50ETF and 50 index of Shanghai Stock Exchange from 2007 to 2016 as data. Because the covariance matrix needs to guarantee the positive definiteness, the general method is to transform the covariance matrix into a positive definite one, and the straightening vector of the covariance matrix is used as the regression variable. However, since the autocorrelation and asymmetry of each element of covariance matrix are not uniform after positive definite transformation and are greatly affected, two methods are proposed in this paper: one is to propose MHAR-diag model. The diagonal element and the non-diagonal element are given different autoregressive coefficients. Based on this model, a smooth transfer function is introduced to characterize the difference between the asymmetry of diagonal element and non-diagonal element. Another method is to consider the non-positive definite transformation. In this paper, a non-positive definite transformation is proposed to be lcor transform, and the model is modeled with positive qualitative constraints. In this paper, DM test and MCS test are used to compare the prediction ability of each model with multiple loss functions. The empirical results show that the prediction ability of the MHAR-diag model can improve the prediction ability of the model under all loss functions, regardless of whether the covariance matrix after logarithmic transformation or lcor transformation can be used to model the MHAR-diag model in comparison with the ordinary MHAR model. The lcor transform proposed in this paper can get better prediction effect than the logarithmic transformation in the same model form. Finally, in the MCS test of the whole model, The MHAR-splitST model with smooth transfer based on lcor transform can predict the optimal performance in the normal fluctuation phase.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51
，
本文编号：2149615
[Abstract]:The development of portfolio and risk management urgently requires the perfection of portfolio theory, and the desire of investors to avoid risks requires the establishment of a more accurate model to predict the risks in the market. The realized covariance matrix of multi-assets based on high-frequency data is a measure of portfolio risk level, and its accurate prediction is an interesting problem. At present, there are many researches on realized volatility models based on high frequency, but because of the limitations of multivariate models, there are few multivariate models based on realized covariance, such as multivariable HAR model and war model. The problem of asymmetry of volatility has been discovered for a long time, which is mainly reflected in the fact that the impact of positive and negative shocks on future volatility is different, and that the impact of good information on volatility is greater than that of good information, which is called leverage effect. In addition, fluctuations have other asymmetries, such as size asymmetry. In order to explain this phenomenon, many researches have introduced smooth transfer into univariate volatility model. Previous studies have proved that smooth transfer can not only improve the fitting degree of the model, but also improve the prediction performance of the model. However, the research of introducing smooth transfer into multivariate volatility model is seriously inadequate, but the empirical study of smooth transfer model based on realized covariance matrix is still a blank field. In this paper, the smooth transfer function is introduced in the MHAR model, which is extended from univariate HAR model to multivariate MHAR model, and the realized covariance matrix of individual stock is modeled by using 7 stocks of 50ETF and 50 index of Shanghai Stock Exchange from 2007 to 2016 as data. Because the covariance matrix needs to guarantee the positive definiteness, the general method is to transform the covariance matrix into a positive definite one, and the straightening vector of the covariance matrix is used as the regression variable. However, since the autocorrelation and asymmetry of each element of covariance matrix are not uniform after positive definite transformation and are greatly affected, two methods are proposed in this paper: one is to propose MHAR-diag model. The diagonal element and the non-diagonal element are given different autoregressive coefficients. Based on this model, a smooth transfer function is introduced to characterize the difference between the asymmetry of diagonal element and non-diagonal element. Another method is to consider the non-positive definite transformation. In this paper, a non-positive definite transformation is proposed to be lcor transform, and the model is modeled with positive qualitative constraints. In this paper, DM test and MCS test are used to compare the prediction ability of each model with multiple loss functions. The empirical results show that the prediction ability of the MHAR-diag model can improve the prediction ability of the model under all loss functions, regardless of whether the covariance matrix after logarithmic transformation or lcor transformation can be used to model the MHAR-diag model in comparison with the ordinary MHAR model. The lcor transform proposed in this paper can get better prediction effect than the logarithmic transformation in the same model form. Finally, in the MCS test of the whole model, The MHAR-splitST model with smooth transfer based on lcor transform can predict the optimal performance in the normal fluctuation phase.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51
，
本文编号：2149615
本文链接：https://www.wllwen.com/kejilunwen/yysx/2149615.html
