非参数乘积误差模型及其对成交量的应用研究

发布时间：2018-06-16 04:01

本文选题：非参数乘积误差模型 + 非参数估计方法　；参考：《西南财经大学》2014年硕士论文

【摘要】：金融计量研究的主要对象为非负值金融时间序列,如波动率、金融持续时间、价格极差、成交量等。针对于这些金融时间序列,学者们提出了—系列的模型进行研究。有刻画波动率的自回归条件异方差模型(ARCH)和广义自回归条件异方差模型(GARCH)、分析持续时间的自回归条件持续时间模型(ACD)以及针对价格极差的条件自回归极差模型(CARR)等。其中,GARCH模型和ACD模型的研究成果最为丰硕。然而,这些模型都是研究单个非负值金融时间序列的。为了能统—研究这些非负值金融时间序列,Engle在2002年首次提出了一种适合于非负值金融时间序列的一般化模型——乘积误差模型(MEM)。GARCH模型、ACD模型以及CARR模型都是乘积误差模型的特例。与参数乘积误差模型相比,非参数乘积误差模型具有自身的优势。参数乘积误差模型容易出现参数误设的问题,而非参数乘积误差模型则能弥补这一缺陷。而且,在数据过程比较复杂的情况下,非参数乘积误差模型的拟合效果通常会优于参数乘积误差模型。回顾以往国内外关于乘积误差方面的文献,我们发现,目前只有关于参数乘积误差方面的研究,非参数乘积误差模型方面的研究还是空白。鉴于此,本文主要致力于研究非参数乘积误差模型,力图完善乘积误差模型的体系。本文主要分为模型理论、模拟试验、实证分析这三块内容。模型理论这部分,我们首先介绍了GAR.CH模型、ACD模型、CARR模型和参数乘积误差模型,比较这四个模型的异同,并详细介绍参数乘积误差模型的估计方法——极大似然估计法。然后构建非参数乘积误差模型,在Buhlmann和McNeil、Cosma和Galli等提出的非参数估计算法的基础上,给出可行的算法,并证明该算法的一致性。该非参数估计方法的一致性证明是本文的一大创新。模拟试验这部分,我们主要运用蒙特卡洛模拟技术,在不同样本容量、随机扰动项服从不同分布、不同的条件均值过程这三种情况下,生成模拟数据。分别建立参数乘积误差模型和非参数乘积误差模型对模拟数据进行估计,比较这两个模型的拟合效果。实证分析这部分,我们将非参数乘积误差模型应用于中国证券市场上,分析上证综指和深证成指的成交量高频数据。针对这两个指数的对数成交量分别建立参数乘积误差模型和非参数乘积误差模型,进行样本内估计和样本外预测,比较这两个模型的拟合效果和预测能力。模拟试验和实证分析的结果均表明,非参数乘积误差模型的拟合效果和预测能力均优于参数乘积误差模型。本论文是国家自然科学基金“新兴订单驱动市场非负值金融时间序列的乘积误差建模及应用研究”(71101118)项目中的子课题。
[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).
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F832.51

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