已實(shí)現(xiàn)協(xié)方差的平滑轉(zhuǎn)移多元異質(zhì)自回歸模型的研究
發(fā)布時(shí)間：2018-07-28 09:11
【摘要】：投資組合和風(fēng)險(xiǎn)管理的發(fā)展迫切要求投資組合理論的完善,而投資者規(guī)避風(fēng)險(xiǎn)的愿望要求構(gòu)建能更加準(zhǔn)確地預(yù)測市場當(dāng)中的風(fēng)險(xiǎn)的模型。基于高頻數(shù)據(jù)的多資產(chǎn)的已實(shí)現(xiàn)協(xié)方差陣作為組合風(fēng)險(xiǎn)水平的一個(gè)度量,其準(zhǔn)確預(yù)測是一個(gè)引人關(guān)注的問題。目前,基于高頻的已實(shí)現(xiàn)波動(dòng)率模型的研究有很多,但是因?yàn)槎嘧兞磕Ｐ偷闹T多限制,基于已實(shí)現(xiàn)協(xié)方差的多變量模型相對而言很少,主要有多變量的HAR模型、WAR模型等。波動(dòng)的不對稱性的問題之發(fā)現(xiàn)已久,其主要體現(xiàn)在過往利好和利空的沖擊對未來波動(dòng)的影響不同,利空信息相對利好信息對波動(dòng)影響更大,此即杠桿效應(yīng)。除此之外,波動(dòng)還具有其他不對稱性,例如大小不對稱性。為了解釋這一現(xiàn)象,已有諸多研究將平滑轉(zhuǎn)移引入單變量波動(dòng)率模型,過往研究證明平滑轉(zhuǎn)移引入單變量的波動(dòng)率模型不僅能提高模型的擬合程度,也能改進(jìn)模型的預(yù)測性能。但是,目前將平滑轉(zhuǎn)移引入多變量波動(dòng)率模型的研究則嚴(yán)重不足,而基于已實(shí)現(xiàn)協(xié)方差陣的平滑轉(zhuǎn)移模型實(shí)證研究則尚為空白領(lǐng)域。本文在由單變量HAR模型擴(kuò)展到多元情況形式的MHAR模型當(dāng)中引入平滑轉(zhuǎn)移函數(shù),并用2007至2016年上證50ETF的7只個(gè)股以及上證50指數(shù)作為數(shù)據(jù),對個(gè)股的已實(shí)現(xiàn)協(xié)方差陣進(jìn)行建模。因?yàn)閰f(xié)方差陣需要保證正定性,故一般做法是對協(xié)方差陣進(jìn)行正定變換,用其變換后的拉直向量作為回歸變量。但由于正定變換后,協(xié)方差陣各個(gè)元素的自相關(guān)性和不對稱性并不統(tǒng)一而且受到很大影響,故本文提出兩種方法:一種是提出MHAR-diag模型,將對角元素和非對角元素賦予不同的自回歸系數(shù),基于這種模型再引入平滑轉(zhuǎn)移函數(shù)以刻畫對角元素和非對角元素不對稱性的不同;另一種方法是考慮非正定變換,本文提出一種非正定變換為lcor變換,并在建立模型時(shí)加以正定性限制條件建模。本文利用DM檢驗(yàn)和MCS檢驗(yàn),利用多個(gè)損失函數(shù)綜合對比各個(gè)模型的樣本外預(yù)測能力。實(shí)證顯示,不論是對經(jīng)對數(shù)變換或lcor變換后的協(xié)方差陣建模,MHAR-diag模型相對于普通的MHAR模型在所有損失函數(shù)下能夠改善模型的預(yù)測能力;同時(shí),本文提出的lcor變換在同樣的模型形式下比對數(shù)變換能得到更好的樣本外預(yù)測效果;最后,在全模型的MCS檢驗(yàn)當(dāng)中,基于lcor變換的加入平滑轉(zhuǎn)移的MHAR-splitST模型綜合而言于正常波動(dòng)階段預(yù)測性能最優(yōu)。
[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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F832.51
，
本文編號：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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F832.51
，
本文編號：2149615
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