本文選題：非參數(shù)乘積誤差模型 + 非參數(shù)估計(jì)方法　； 參考：《西南財(cái)經(jīng)大學(xué)》2014年碩士論文

【摘要】：金融計(jì)量研究的主要對(duì)象為非負(fù)值金融時(shí)間序列,如波動(dòng)率、金融持續(xù)時(shí)間、價(jià)格極差、成交量等。針對(duì)于這些金融時(shí)間序列,學(xué)者們提出了—系列的模型進(jìn)行研究。有刻畫(huà)波動(dòng)率的自回歸條件異方差模型(ARCH)和廣義自回歸條件異方差模型(GARCH)、分析持續(xù)時(shí)間的自回歸條件持續(xù)時(shí)間模型(ACD)以及針對(duì)價(jià)格極差的條件自回歸極差模型(CARR)等。其中,GARCH模型和ACD模型的研究成果最為豐碩。然而,這些模型都是研究單個(gè)非負(fù)值金融時(shí)間序列的。為了能統(tǒng)—研究這些非負(fù)值金融時(shí)間序列,Engle在2002年首次提出了一種適合于非負(fù)值金融時(shí)間序列的一般化模型——乘積誤差模型(MEM)。GARCH模型、ACD模型以及CARR模型都是乘積誤差模型的特例。 與參數(shù)乘積誤差模型相比,非參數(shù)乘積誤差模型具有自身的優(yōu)勢(shì)。參數(shù)乘積誤差模型容易出現(xiàn)參數(shù)誤設(shè)的問(wèn)題,而非參數(shù)乘積誤差模型則能彌補(bǔ)這一缺陷。而且,在數(shù)據(jù)過(guò)程比較復(fù)雜的情況下,非參數(shù)乘積誤差模型的擬合效果通常會(huì)優(yōu)于參數(shù)乘積誤差模型�；仡櫼酝鶉�(guó)內(nèi)外關(guān)于乘積誤差方面的文獻(xiàn),我們發(fā)現(xiàn),目前只有關(guān)于參數(shù)乘積誤差方面的研究,非參數(shù)乘積誤差模型方面的研究還是空白。 鑒于此,本文主要致力于研究非參數(shù)乘積誤差模型,力圖完善乘積誤差模型的體系。本文主要分為模型理論、模擬試驗(yàn)、實(shí)證分析這三塊內(nèi)容。模型理論這部分,我們首先介紹了GAR.CH模型、ACD模型、CARR模型和參數(shù)乘積誤差模型,比較這四個(gè)模型的異同,并詳細(xì)介紹參數(shù)乘積誤差模型的估計(jì)方法——極大似然估計(jì)法。然后構(gòu)建非參數(shù)乘積誤差模型,在Buhlmann和McNeil、Cosma和Galli等提出的非參數(shù)估計(jì)算法的基礎(chǔ)上,給出可行的算法,并證明該算法的一致性。該非參數(shù)估計(jì)方法的一致性證明是本文的一大創(chuàng)新。模擬試驗(yàn)這部分,我們主要運(yùn)用蒙特卡洛模擬技術(shù),在不同樣本容量、隨機(jī)擾動(dòng)項(xiàng)服從不同分布、不同的條件均值過(guò)程這三種情況下,生成模擬數(shù)據(jù)。分別建立參數(shù)乘積誤差模型和非參數(shù)乘積誤差模型對(duì)模擬數(shù)據(jù)進(jìn)行估計(jì),比較這兩個(gè)模型的擬合效果。實(shí)證分析這部分,我們將非參數(shù)乘積誤差模型應(yīng)用于中國(guó)證券市場(chǎng)上,分析上證綜指和深證成指的成交量高頻數(shù)據(jù)。針對(duì)這兩個(gè)指數(shù)的對(duì)數(shù)成交量分別建立參數(shù)乘積誤差模型和非參數(shù)乘積誤差模型,進(jìn)行樣本內(nèi)估計(jì)和樣本外預(yù)測(cè),比較這兩個(gè)模型的擬合效果和預(yù)測(cè)能力。模擬試驗(yàn)和實(shí)證分析的結(jié)果均表明,非參數(shù)乘積誤差模型的擬合效果和預(yù)測(cè)能力均優(yōu)于參數(shù)乘積誤差模型。 本論文是國(guó)家自然科學(xué)基金“新興訂單驅(qū)動(dòng)市場(chǎng)非負(fù)值金融時(shí)間序列的乘積誤差建模及應(yīng)用研究”(71101118)項(xiàng)目中的子課題。
[Abstract]:The main objects of financial econometrics are non-negative financial time series, such as volatility, financial duration, poor price, trading volume and so on. In view of these financial time series, scholars put forward-series model to study. The autoregressive conditional heteroscedasticity model (ARCH) and the generalized autoregressive conditional heteroscedasticity model (GARCHG), the autoregressive conditional duration model (ACDD), and the conditional autoregressive range model (CARR) for price range are presented. The research results of GARCH model and ACD model are the most fruitful. However, these models are used to study a single non-negative financial time series. In order to integrate and study these non-negative financial time series, Engle first proposed a generalized model for non-negative financial time series in 2002. The product error model is the product error model and the ACD model and the Carr model are both products. The special case of error model. Compared with the parametric product error model, the nonparametric product error model has its own advantages. The parametric product error model is prone to the problem of parameter missetting, but the non-parametric product error model can make up for this defect. Moreover, when the data process is complex, the fitting effect of the non-parametric product error model is usually better than that of the parametric product error model. Reviewing the previous literatures on product error at home and abroad, we find that only the research on parametric product error and the research on non-parametric product error model are still blank. In view of this, this paper is mainly devoted to the study of non-parametric product error model, trying to perfect the system of product error model. This paper is divided into three parts: model theory, simulation experiment and empirical analysis. In this part of model theory, we first introduce GAR.CH model / ACD model / Carr model and parameter product error model, compare the similarities and differences of these four models, and introduce in detail the estimation method of parametric product error model, the maximum likelihood estimation method. Then the nonparametric product error model is constructed. Based on the nonparametric estimation algorithms proposed by Buhlmann and McNeilman Cosma and Galli, a feasible algorithm is proposed, and the consistency of the algorithm is proved. The consistency proof of this nonparametric estimation method is a great innovation in this paper. In this part of the simulation experiment, we mainly use Monte Carlo simulation technology to generate simulation data under the three conditions of different sample size, random disturbance terms from different distribution, different conditional mean process. The parametric product error model and the non-parametric product error model were established to estimate the simulated data, and the fitting results of the two models were compared. In this part, we apply the non-parametric product error model to the Chinese stock market to analyze the high frequency data of the trading volume of the Shanghai Composite Index and Shenzhen Composite Index. According to the logarithmic trading volume of the two indices, the parametric product error model and the non-parametric product error model are established, respectively. The intra-sample estimation and extrasample prediction are carried out, and the fitting effect and prediction ability of the two models are compared. The results of simulation experiments and empirical analysis show that the fitting effect and prediction ability of the non-parametric product error model are better than that of the parametric product error model. This thesis is a subtopic of the project of "Product error Modeling and Application Research of Non-negative Financial time Series in emerging order-driven Market" of National Natural Science Foundation of China (71101118).
【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：F224;F832.51

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