分位数回归模型及在金融经济中的应用

发布时间：2018-01-06 12:37

本文关键词：分位数回归模型及在金融经济中的应用　出处：《合肥工业大学》2016年博士论文　论文类型：学位论文

【摘要】：金融经济系统是一个复杂系统,往往表现出典型的复杂性特征(如非线性、非平稳性和异质性等)。其中,异质性特征是指受政策环境、市场竞争及技术创新等因素影响,不同系统之间、以及同一系统内部存在不同的运行规律和内在特质,该特征已成为金融经济系统中众多复杂现象的重要突破点之一。与传统的均值回归方法相比,分位数回归(QR)在异质性建模方面提供了一个基本的分析工具,能够揭示解释变量对响应变量在不同分位点处的异质影响,从而更好地逼近和揭示真实金融经济系统在不同环境下的运行规律,具有重要的理论意义和实践价值。本文选取“分位数回归的理论模型及其在金融经济中的应用”这一研究主题,综合应用管理学、统计学和计量经济学等学科知识,采取理论分析、数值模拟和实证研究相结合的方法,从以下两方面开展研究：一是在理论建模方面,对经典的分位数回归模型进行拓展；二是在应用研究方面,选取金融经济领域的热点问题,在分位数回归框架下开展相关主题研究。论文的主要工作和创新点如下：1)在线性分位数回归建模方面,将误差校正模型从均值框架推广到分位数框架。首先,提出分位数误差校正模型(QECM)的概念,并给出其一整套建模技术：模型表示、参数估计、模型定阶、诊断检验和模型预测(包括条件分位数预测与条件密度预测)；然后,通过数值模拟,研究QECM预测能力,并将其与经典的均值误差校正模型(MECM)、分位数自回归模型(QAR)进行对比,发现前者能够极大地提高预测的精度和准度；最后,将模型应用于宏观经济管理,讨论中国货币供应对物价水平的影响,实证检验了QECM的条件密度预测能力。2)在非线性分位数回归建模方面,研究门限分位数自回归模型(TQAR)。首先,给出了TQAR的模型定阶方法,推导了门限值估计量的渐近分布,并在此基础上构造出门限效应的似然比检验。然后,通过数值模拟,研究TQAR的参数估计性质及模型预测能力,通过与TAR、TAR-GARCH以及QAR等模型对比,发现前者在门限值估计、回归系数估计的样本表现方面都优于后者,并且前者在预测的精度和准度方面都更具优势。最后,将模型应用于实证研究,一是讨论其在中国股市收益自相关性分析的应用,发现收益序列呈现出典型的门限效应和异质效应；二是使用该模型来研究中国通货膨胀的非线性动态特征,并给出通货膨胀波动趋势的条件密度预测。3)在非平稳时间序列分位数回归建模方面,基于分位数协整理论,检验中国“费雪效应”的存在性及异质性。定量研究在不同分位点处名义利率和通货膨胀之间真实回归关系,并建立相应的分位数误差校正模型,用于刻画名义利率由短期波动向长期均衡动态调整速度在不同分位点处的差异。结论表明,基于分位数协整方法能够得到比传统均值协整检验更为深刻的结果,不仅能够检验出中国经济系统在哪些状态(分位点)下存在“费雪效应”及“费雪效应”的强弱,而且能够通过不同状态下的调整速度差异,全面地刻画“费雪效应”的异质性。4)在“贫信息”数据的预测建模方面,将分位数回归与灰色预测模型相结合,建立基于中位数回归的灰色预测系列模型：LAD-GM(1,1)模型、LAD-GM(2,1)模型、LAD-GM(1,1)幂模型及LAD-MGM(1,m)模型,并给出参数估计方法。通过与传统的最小二乘准则比较,发现本文提供的方法不仅能够有效提高模型的预测精度,而且能够克服最小二乘准则下参数估计稳健性较差、易出现病态性的缺点,充分提高各类灰色预测模型的适用性。
[Abstract]:The financial system is a complex system, often shows the complexity of the typical characteristics (such as nonlinear, non-stationary and heterogeneity). The heterogeneity refers to the policy environment, market competition and technology innovation, between different systems, and within the same system has different operation rules and the internal qualities, this feature has become one of the important breakthrough point of financial and economic system in many complex phenomena. Compared with the traditional regression method, quantile regression (QR) in heterogeneous modeling provides a basic analysis tool, can explain heterogeneity variables on response variables in different site influence thus, a better approximation and reveal the operation principle of real financial and economic system in different environment, has important theoretical significance and practical value. This paper selects the "theoretical model and quantile regression The theme of the application in the financial economy, comprehensive application of management science, statistics and Econometrics knowledge, through theoretical analysis, numerical simulation and empirical research, carried out the research from the following two aspects: one is the theory of quantile modeling, classical regression model is extended; the two is in the aspect of application research, selection of hot issues of the economic and financial areas to carry out related research topics in the quantile regression framework. The main work and innovation are as follows: 1) in the linear quantile regression model, the error correction model from the quantile framework extended to mean framework. First, put forward the quantile error the correction model (QECM) concept, and gives a set of modeling techniques: model, parameter estimation, model order, diagnostic test and prediction model (including the number and condition condition prediction Then, through density prediction); numerical simulation research on QECM predictive ability, and the mean error correction model of the classic (MECM), quantile autoregressive model (QAR) were compared, it was found that the former can greatly improve the prediction precision and accuracy; finally, the model is applied to macroeconomic management. Discuss the Chinese money supply impact on the price level, the empirical test of the conditional density of the prediction ability of QECM.2) in the nonlinear quantile regression model, study the threshold quantile autoregressive model (TQAR). Firstly, the method of TQAR model order determination was given, deduces the threshold estimation asymptotic distribution quantity, and on the basis of constructed by the likelihood ratio test for threshold effect. Then, through numerical simulation, model parameter estimation and prediction ability of the nature of TQAR, with TAR, TAR-GARCH and QAR model comparison, found that the former in threshold value estimation, back The sample performance regression coefficient estimation is better than the latter, and the former in the prediction of the precision and accuracy of both advantages. Finally, the model is applied to the empirical study, the first one is to discuss its application in revenue Chinese stock market since the correlation analysis, found that the threshold effect and heterogeneous effect return series show the typical two; nonlinear dynamic characteristics of Chinese inflation, the use of the model, and gives the conditions of density fluctuations trend inflation forecast.3) in non-stationary time series quantile regression modeling, quantile cointegration test based on the theory of Chinese, "Fisher Effect" and the existence of heterogeneity. The quantitative study in different sites between the nominal interest rate the real and inflation regression, and establish quantile error correction model, used to describe the nominal interest rate from short-term fluctuation to long-term equilibrium dynamic adjustment speed The difference in different sites. The conclusion shows that the quantile cointegration method can get more profound results than traditional mean cointegration test based on not only can test Chinese economic system in which the state (quantile) under the "Fisher Effect" and "Fisher Effect" of the strength, but also by difference adjustment the speed under different conditions, fully describe the heterogeneity of.4 Fisher Effect ") in the aspect of" modeling poor information "data, the quantile regression and grey prediction model are combined to establish the grey forecast model based on median regression series: LAD-GM (1,1) model, LAD-GM (2,1) model, LAD-GM (1,1) power model and LAD-MGM (1, m) model, and gives the parameter estimation method. Through the comparison with the traditional least squares criterion, found the method provided in this paper can not only improve the prediction accuracy of the model, but also can grams Under the least square criterion, the robustness of the parameter estimation is poor, and the ill condition is easy to appear, and the applicability of the grey prediction model is fully improved.

【学位授予单位】：合肥工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224;F822.5;F832.51

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