本文關(guān)鍵詞：非參數(shù)條件自回歸極差模型及其應用　出處：《西南財經(jīng)大學》2013年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 極差 波動率 參數(shù)CARR(1 1)模型 非參數(shù)CARR(1 1)模型

【摘要】：近幾年,我國證券市場正處在一個機遇和風險并存的時代,投融資環(huán)境十分地復雜,投資者如何有效地控制和管理其在股票市場上的投資風險,起著關(guān)鍵性的作用。證券市場自產(chǎn)生以來就以其價格的波動為主要特征,如何準確地描述證券市場的價格以及確定市場未來收益率的情況是證券市場各利益主體所關(guān)心的問題。因此,對波動性的研究具有重要的理論意義與應用價值。 眾所周知,用波動率來刻畫金融市場的波動性,在理論領(lǐng)域和應用領(lǐng)域都受到了國內(nèi)外學者的廣泛關(guān)注,成為現(xiàn)代金融經(jīng)濟學和計量經(jīng)濟學領(lǐng)域的重要課題。上世紀50年代,波動率就在資本資產(chǎn)定價模型和期權(quán)定價模型中扮演著重要的角色�？傊�,波動率不但對投資者的投資行為產(chǎn)生了重要影響,而且還在資產(chǎn)價格確定、績效評估等經(jīng)濟學領(lǐng)域得到了普遍的應用。雖然國內(nèi)外學者對于用波動率來刻畫金融市場波動性方面的研究已經(jīng)十分地廣泛,研究內(nèi)容不僅涉及到了一元、多元GARCH模型,還涉及到了參數(shù)、非參數(shù)和半?yún)?shù)GARCH模型。國內(nèi)外學者對于用極差來刻畫金融市場波動性的研究卻不多,這方面的研究多數(shù)停留在參數(shù)CARR模型領(lǐng)域,而在非參數(shù)CARR模型領(lǐng)域卻很少涉及。 國內(nèi)外相關(guān)文獻指出,極差比波動率能夠更好地刻畫金融市場的波動性。因而,本文將利用極差和波動率的關(guān)系,結(jié)合參數(shù)CARR模型和非參數(shù)GARCH模型的思想,提出非參數(shù)CARR模型及其在比較弱的條件下的一致收斂估計方法,并對其估計的一致性進行證明；然后分別從模擬角度和實證角度,對參數(shù)CARR(1,1)模型和非參數(shù)CARR(1,1)模型進行模擬研究和實證分析,研究哪個模型能夠更好地刻畫金融市場的波動性。一方面,有利于充實金融市場計量經(jīng)濟學、時間序列分析和高頻數(shù)據(jù)的研究內(nèi)容和研究方法；另一方面,結(jié)合當前我國證券市場的情況考慮,實證研究結(jié)果對于了解投資者、市場交易活動受市場結(jié)構(gòu)和交易制度的影響程度以及完善我國證券市場的監(jiān)管措施,有效地提高市場的交易質(zhì)量提供了科學的決策依據(jù),具有重要的實際應用價值。本文的主要結(jié)構(gòu)安排如下： 第一,理論部分。首先,介紹參數(shù)CARR模型及其估計方法；然后,利用極差和波動率之間的關(guān)系,結(jié)合參數(shù)CARR模型和非參數(shù)GARCH模型的思想,提出非參數(shù)CARR模型及其在比較弱的條件下的一致收斂估計方法,并對其估計的一致性進行證明。該部分將CARR模型由參數(shù)領(lǐng)域向非參數(shù)領(lǐng)域進行了擴展,為本文在模型和估計方法上的創(chuàng)新。 第二,模擬研究。為了能夠更好地模擬金融市場的極差序列和杠桿效應以及加強論證的有效性和科學性,本文將通過3種數(shù)據(jù)生成過程和2種擾動項分布分別生成長度n=500的極差序列和真實波動率序列；然后將上述數(shù)據(jù)生成過程循環(huán)計算500次,運用預測能力評價指標比較參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型的擬合能力,研究哪個模型能夠更好地擬合真實波動率序列。該部分通過模擬發(fā)現(xiàn)了非參數(shù)CARR (1,1)模型的擬合能力優(yōu)于參數(shù)CARR (1,1)模型,為后面將參數(shù)CARR (1,1)模型和非參數(shù)CARR(1,1)模型運用到我國滬深300指數(shù)中進行具體的實證研究,奠定了理論基礎(chǔ)。 第三,實證分析。本文將選取滬深300指數(shù)日極差序列作為研究對象,將整個樣本分為樣本期內(nèi)和樣本期外兩部分,從描述性統(tǒng)計特征分析、模型估計、預測能力評價指標和MZ回歸方程幾個方面比較參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型樣本期內(nèi)和樣本期外的預測能力。該部分從實證角度證明了非參數(shù)CARR (1,1)模型的擬合能力優(yōu)于參數(shù)CARR (1,1)模型,對模擬結(jié)果進行了驗證,結(jié)果更具有說服力。 以上幾個步驟逐層遞進、環(huán)環(huán)相扣。圍繞參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型進行了系統(tǒng)的研究,得出以下幾點重要結(jié)論。 第一,非參數(shù)CARR模型的估計方法具有在比較弱的條件下一致收斂的性質(zhì)。 第二,無論通過哪種數(shù)據(jù)生成過程和擾動項分布,經(jīng)過m=500次循環(huán)計算后,得到的非參數(shù)CARR (1,1)模型的預測誤差均要小于參數(shù)CARR (1,1)模型的預測誤差；無論通過哪種數(shù)據(jù)生成過程,當擾動項服從Weibull(1,1.5)分布時得到的極差序列和真實波動率序列,通過m=500次循環(huán)計算后所得到的非參數(shù)CARR (1,1)模型的預測誤差的減少程度大于參數(shù)CARR (1,1)模型的預測誤差的減少程度(個別指標除外)；無論通過哪種數(shù)據(jù)生成過程,當擾動項服從Weibull(1,1.5)分布時得到的極差序列和真實波動率序列,通過m=500次循環(huán)計算后所得到的參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型的預測誤差均要小于擾動項服從指數(shù)分布exp(1)時的預測誤差。 第三,基本統(tǒng)計特征顯示,滬深300指數(shù)極差序列具有明顯的波動聚集現(xiàn)象和高階的ARCH效應,存在正偏、分布擴散和拖尾的現(xiàn)象。 第四,樣本期內(nèi)的極差具有不同程度的自相關(guān)性,有的具有短記憶性,有的具有長記憶性和可持續(xù)性；自相關(guān)系數(shù)和偏相關(guān)系數(shù)大致上呈現(xiàn)出隨著滯后階數(shù)的增加逐漸衰減的特點,其中偏相關(guān)系數(shù)的衰減程度大于自相關(guān)系數(shù)的衰減程度；Ljung-Box Q統(tǒng)計量呈現(xiàn)出隨著滯后階數(shù)的增加逐漸增加的特點。 第五,通過對參數(shù)CARR (1,1)模型進行樣本期內(nèi)的極大似然估計,發(fā)現(xiàn)在5%的顯著性水平下,估計參數(shù)的T值均是顯著的；經(jīng)過參數(shù)CARR(1,1)模型過濾之后,樣本期內(nèi)的極差序列已經(jīng)不存在顯著地異方差性；參數(shù)CARR(1,1)模型可以很好地擬合樣本期內(nèi)滬深300指數(shù)的波動性；滬深300指數(shù)存在很強的波動聚集現(xiàn)象。 第六,預測能力評價指標和MZ回歸方程顯示,無論“己實現(xiàn)波動率”采用哪種方式測度,樣本期內(nèi)和樣本期外非參數(shù)CARR (1,1)模型的預測能力均優(yōu)于參數(shù)CARR (1,1)模型。 與其他文章相比,本文的創(chuàng)新點主要基于以下三方面： 第一,本文利用極差和波動率之間的關(guān)系,結(jié)合參數(shù)CARR模型和非參數(shù)GARCH模型的思想,首次提出非參數(shù)CARR模型及其在比較弱的條件下的一致收斂估計方法,并對其估計方法的一致性進行證明。該部分將CARR模型由參數(shù)領(lǐng)域向非參數(shù)領(lǐng)域進行了擴展,為本文在模型和估計方法上的理論創(chuàng)新。 第二,首次對參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型進行模擬研究。為了能夠更好地模擬金融市場的極差序列和杠桿效應以及加強論證的有效性和科學性,本文通過選取不同的數(shù)據(jù)生成過程和擾動項分布來對參數(shù)CARR(1,1)模型和非參數(shù)CARR(1,1)模型進行模擬研究和預測能力評價,通過模擬發(fā)現(xiàn)非參數(shù)CARR (1,1)模型的擬合能力優(yōu)于參數(shù)CARR (1,1)模型,能夠更好地擬合真實波動率序列。該部分為將非參數(shù)CARR (1,1)模型運用到金融市場中進行具體的實證研究奠定了良好的理論基礎(chǔ)。 第三,首次將非參數(shù)CARR (1,1)模型運用到我國滬深300指數(shù)極差序列中進行實證研究。本文將滬深300指數(shù)極差序列分為樣本期內(nèi)和樣本期外兩部分,通過將參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型運用到我國滬深300指數(shù)極差序列中進行基本統(tǒng)計特征分析、模型估計和預測能力評價,一方面發(fā)現(xiàn)了滬深300指數(shù)極差序列存在顯著的正偏、分布擴展和波動聚集的現(xiàn)象；另一方面,通過對參數(shù)CARR (1,1)模型和非參數(shù)CARR (1,1)模型進行樣本期內(nèi)和樣本期外的預測能力評價和MZ回歸,發(fā)現(xiàn)非參數(shù)CARR(1,1)模型的預測能力優(yōu)于參數(shù)CARR (1,1)模型,能夠更好地刻畫我國滬深300指數(shù)的波動性。該部分從實際應用角度對模擬結(jié)果進行驗證,結(jié)果更具有說服力。 本文由2011年度國家自然科學基金青年科學基金項目《新興訂單驅(qū)動市場非負值金融時間序列的乘積誤差建模及應用研究》(71101118)和2009年度教育部人文社會科學研究青年基金項目《新興訂單驅(qū)動市場金融持續(xù)時間的統(tǒng)計分析及其應用》(09YJC910009)資助完成。
[Abstract]:In recent years, China's securities market is in a era of opportunities and risks, the financing environment is very complex, investors how to effectively control and manage the investment risk in the stock market, plays a key role. The stock market has been in the price fluctuation of main features how to accurately describe the securities market, the price and the market determine the future yield are the interests of the main stock market concerns. Therefore, the study of volatility has important theoretical significance and practical value.
As everyone knows, the volatility of volatility to describe the financial market, in the field of theory and application have attracted the attention of scholars at home and abroad, has become an important topic in modern financial economics and Econometrics field. In 50s the last century, volatility in the pricing model and option pricing model of capital assets plays an important role. In short, volatility not only has important influence on the investment behavior of investors, but also asset price determination, performance evaluation and other areas of economics has been widely used. Although scholars at home and abroad with the wave rate to describe the volatility of financial market is very wide, not only involves the contents of one yuan the multivariate GARCH model, and also involves parameters, non parametric and semi parametric GARCH model. Scholars to describe the volatility of financial market with the poor But not much, most of this research stays in the domain of parameter CARR model, but is rarely involved in the nonparametric CARR model domain.
The related literature at home and abroad, pointed out that the fluctuation range than the volatility can better describe the financial market. Therefore, this paper will use the relationship between range and volatility, combined with the parameters of CARR model and non parametric GARCH model, the nonparametric CARR model and uniform convergence in a weak estimation method under, and the consistency of the estimates are proved; then from the simulation and empirical point of view, the parameters of CARR (1,1) model and non parameter CARR (1,1) model for simulation study and empirical research on the volatility of which model can better depict financial market. On the one hand, is conducive to enrich the financial market econometrics, research contents and research methods of time series analysis and high frequency data; on the other hand, considering the current situation of China's securities market, the empirical results for the understanding of investors, market transactions It is a scientific decision basis for us to be influenced by the market structure and trading system and improve the regulation measures in China's securities market, and effectively improve the trading quality of the market. It has important practical application value. The main structure of this paper is as follows:
First, the theoretical part. Firstly, introducing the model and parameter estimation method of CARR; then, the relationship between range and volatility, combined with the parameters of CARR model and non parametric GARCH model, the nonparametric CARR model and uniform convergence in the weak condition estimation method, and the consistency of estimation this part will be proved. The CARR model parameters from the field to the non parameter field is extended to the innovation in the model and estimation methods.
Second, simulation research. In order to poor sequence and leverage effect can better simulate the financial market and strengthen the demonstration of effective and scientific, the 3 kinds of data generation process and 2 kinds of disturbance distribution respectively generate length n=500 sequence and the range of actual volatility sequence; then the data generation process cycle calculation 500, the use of prediction ability evaluation index comparison of parameters of CARR (1,1) model and non parameter CARR (1,1) model fitting ability, which study model can better fit the actual volatility sequence. This part is found through the dynamic simulation of non parameter CARR (1,1) fitting ability is better than the parameters of the CARR model (1,1) model for behind the parameters of CARR (1,1) model and non parameter CARR (1,1) model is applied to the empirical research of China's Shanghai and Shenzhen 300 index, which lay a theoretical foundation.
Third, empirical analysis. This paper will select the Shanghai and Shenzhen 300 index range sequence as the research object, the entire sample is divided into two parts of the sample period and sample period, from the characteristics of descriptive statistics analysis, model estimation, prediction ability evaluation index and MZ regression equation on compare parameters of CARR (1,1) model and non parametric CARR (1,1) model of sample period and sample period. In this part, from the perspective of the empirical proof of non parameter CARR (1,1) fitting ability is better than the parameters of the CARR model (1,1) model, the simulation results were verified, the results more convincing.
The above steps step by step, interlocking. The following conclusions are drawn from the parametric CARR (1,1) model and the non parametric CARR (1,1) model.
First, the estimation method of the nonparametric CARR model has the property of uniform convergence under relatively weak conditions.
Second, no matter what kind of data through the production process and the disturbance distribution, after m=500 cycles after the calculation, the parameters of CARR (1,1) prediction error model parameters were less than CARR (1,1) prediction error model; the generating process of either data, when the disturbance obeys the Weibull distribution (1,1.5) the range of sequences and real volatility series, non parametric CARR obtained by m=500 cycles after computation (1,1) to reduce the degree of model prediction error is larger than the parameters of CARR (1,1) to reduce the degree of model prediction error (the individual indicators except); either the data generation process, when the disturbance to Weibull (1,1.5) distribution obtained when the range data and real volatility series, CARR parameters obtained by m=500 cycles after calculating (1,1) model and non parameter CARR (1,1) model prediction errors are less than the disturbance service The prediction error from the exponential distribution of exp (1).
Third, the basic statistical characteristics show that the Shanghai and Shenzhen 300 index extreme sequence has obvious volatility aggregation phenomenon and high-order ARCH effect, and there are positive bias, distribution diffusion and tailing phenomenon.
Fourth, poor sample period has different degree of correlation, with some short memory, some has long memory and sustainability; self correlation coefficient and partial correlation coefficient generally showed with the increase of the characteristics of lag order decays, the attenuation degree of the partial correlation coefficient is greater than the degree of attenuation of autocorrelation the coefficient of Ljung-Box; Q statistics show with the characteristics of increasing the number of lags increases gradually.
Fifth, the parameters of CARR (1,1) model for maximum likelihood estimation in the sample period, found in the 5% level of significance, the parameter estimation of T value was significant; after the parameters of CARR (1,1) model after filtering, the range sequence sample period has significant heteroscedasticity parameter; CARR (1,1) model can well fit the volatility of the sample period of the Shanghai and Shenzhen 300 index; there is very strong aggregation fluctuation in the CSI 300 index.
Sixth, show the ability to predict the evaluation index and MZ regression equation, regardless of the realized volatility measure "by which way, the sample period of sample period and non parameter CARR (1,1) model parameters are better than CARR (1,1) model.
Compared with other articles, the innovation of this article is mainly based on the following three aspects:
First, the relationship between range and volatility, combined with the parameters of CARR model and non parametric GARCH model, nonparametric CARR model is proposed for the first time and the uniform convergence under weak conditions estimation method, and the consistency of the estimation method is proved. The CARR model parameters from the field to the non the parameter field is extended to the theoretical innovation in the model and the method of estimation.
Second, for the first time on the parameters of CARR (1,1) model and non parameter CARR (1,1) model simulation. In order to poor sequence and leverage effect can better simulate the financial market and strengthen the demonstration of effective and scientific, this paper selected the data generation process and different disturbance distribution parameters of CARR (1,1) model and non parameter CARR (1,1) to evaluate the simulation and prediction ability of the model, according to the simulation parameters of CARR (1,1) fitting ability is better than the parameters of the CARR model (1,1) model can better fit the actual volatility sequence. This part is the non parameter CARR (1,1) model is applied to the financial market lay a good theoretical basis for the empirical research.
Third, for the first time the parameters of CARR (1,1) model is applied to the Shanghai and Shenzhen 300 index range in the sequence of empirical research. In this paper, the Shanghai and Shenzhen 300 index range sequence is divided into two parts of the sample period and the sample period, the parameters of CARR (1,1) model and non parameter CARR (1,1) model is applied to China's Shanghai and Shenzhen 300 index range in the sequence analysis of basic statistical characteristics, model estimation and prediction ability evaluation, on the one hand that the Shanghai and Shenzhen 300 index range sequence is positively biased, aggregated distribution expansion and fluctuation phenomenon; on the other hand, based on the parameters of CARR (1,1) model and non parametric model to evaluate CARR (1,1) the prediction ability of the sample period and sample period and MZ regression, found that the parameters of CARR (1,1) prediction ability is superior to the parameters of the CARR model (1,1) model can better depict China's Shanghai and Shenzhen 300 index volatility. The part from the practical The results are verified with the angle, and the results are more convincing.
This paper is composed of 2011 National Natural Science Foundation of China project "new order driven product error modeling and Application Research on the market > non negative financial time series (71101118) and the 2009 year of Ministry of education, humanities and social science research youth fund project" emerging market financial order driven the duration of the statistical analysis and application "(09YJC910009) funding to complete.

【學位授予單位】：西南財經(jīng)大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F224;F832.51

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