混频数据回归模型的建模理论、分析技术研究

发布时间：2018-01-20 10:37

本文关键词： 混频数据 MIDAS类模型估计方法 EQW模型季度GDP 通货膨胀资产价格　出处：《东北财经大学》2016年博士论文　论文类型：学位论文

【摘要】：传统计量经济模型在分析时间序列数据所表示的变量时,无论是模型的构建,还是具体应用过程均暗含一个重要假定,即选取的变量样本数据必须具有同频率特性,否则模型无法识别,传统计量经济模型对指标数据同频率的要求及实际中基础数据频率的不一致性往往会使研究人员陷入进退两难的境地,特别是在金融市场,微观经济与宏观经济紧密结合的今天,政策制定者和研究人员急需一种模型在少损失有效信息情况下能够将高频宏观经济数据、超高频金融数据与低频宏观经济数据桥接起来,正式在这种传统理论模型应用处于瓶颈,实际经济中不同频率时间序列数据日新月异的背景下,混频数据计量经济模型分析技术及重要性逐渐凸显出来。为了更好的引进,发展混频数据模型的建模理论,分析技术及应用等领域的研究,本论文深入剖析了混频数据回归模型(MIDAS)的内部结构,并与传统分布滞后模型作对比分析,指出MIDAS模型与传统回归模型的区别与联系,在此基础上系统梳理了 MIDAS模型的各种不同形式,多种不同形式的权重函数;结合数值化最优算法给出了 MIDAS类模型常用非线性最小二乘及最大似然估计方法的具体机理及演绎过程;随后依据传统分布滞后模型的识别方法,结合范德蒙矩阵推导出了 MIDAS类模型的新估计方法(普通最小二乘法),给出了混频模型参数含义的理论基础,权重函数的实际意义,并将MIDAS类模型应用于实际经济分析中。在MIDAS类模型应用方面,由于权重函数的选择对于MIDAS模型至关重要,本论文克服了以往关于MIDAS模型研究中只选取单一权重函数的不足,全面考虑了五种不同权重函数形式,并以此构建MIDAS类模型及非限制MIDAS类模型研究了我国具有不同频率指标,存在较大争议的经济领域中,同时与传统计量经济模型做比较分析。具体包括以下几个部分:第一:根据最初提出的混频数据预测模型设置原理,结合传统时间序列回归模型推导出了混频数据回归模型的基本形式及拓展形式;主要包括一元混频数据回归模型,多元混频数据回归模型,自回归多元混频数据模型,非限制混频数据回归模型,混频数据因子回归模型、混频数据误差修正模型,混频数据马尔可夫区制转移模型、混频向量自回归模型等。指出权重函数的设计思想,概括、梳理出多种权重函数具体形式,并剖析每种权重函数的性质及实用条件,在此基础上,根据Beta密度函数设计了新权重函数。第二:阐述了 MIDAS类模型常用估计方法的内在机理,从理论上推导出了 MIDAS模型的非线性最小二乘NLS法,给定初始值,依据MIDAS模型目标函数的具体形式,导出参数估计的迭代公式,通过限定终止条件找到收敛解,根据目标函数的性质,主要讨论目标函数为无约束条件的极小化,与NLS结合的数值最优化算法,包括牛顿法,高斯牛顿法,拟牛顿法等,同时指出了这些方法的适用条件,运算效率及优缺点。采用上述NLS估计方法,根据指标数据时间属性,构建了包含日数据,月度数据及季度数据的六种多元混频数据回归模型,分析了我国高频资产价格波动与宏观经济增长、通货膨胀的关系。首先在分析高频资产价格对经济增长的影响效应及作用路径时,预测结果的对比分析显示:基于Almon指数权重函数构建的Exp Almon-AR-M-MIDAS模型能够提取更多高频变量股票价格的日数据信息,其拟合效果及样本内预测精度表现最优,实证结果表明:高频资产价格对我国经济增长的影响效应显著,并且存在正负交替两种作用路径,能够对经济增长起到提前预警作用。其中房地产价格的影响效应大于股票价格,股票价格对经济的影响方向存在不稳定性。其次在分析高频变量股票价格对通货膨胀的作用机制及预测效果时,实证结果表明:五种不同权重函数中快速下降的Beta-权重函数无论是拟合效果还是预测精度上都具有比较优势,以此构建的混频数据回归模型在中国通货膨胀的月度预报方面具有较高的时效性和精确性,高频资产价格股票价格对我国通货膨胀影响效应显著,随着滞后阶数的增加股票价格对通货膨胀的影响程度呈迅速下降趋势。其预测效果优于同频率的传统计量模型和其他混频数据模型。第三:给出了MIDAS模型极大似然估计方法,识别原理及具体过程;结合传统极大似然估计和MIDAS模型具体形式系统推导了 MIDAS-ML估计量及其渐进分布,并给出MIDAS-ML估计量方差协方差矩阵简化形式,根据推导预检验估计量设置MIDAS模型参数的统计检验方法。采用此估计方法,构建六种MIDAS考察了货币政策的传导机制及有效性,货币政策对经济增长的影响效果和传递路径,实证结果表明:以货币供应量为代表的货币政策显著影响经济增长,短期内,扩张的货币政策能够拉动经济增长,长期内,特别是26个月直至37个月,货币政策对经济增长再次发挥出促进作用。第四:结合传统分布滞后模型的估计方法,根据MIDAS模型的内在机理,推导出了 MIDAS模型,M-MIDAS模型,U-MIDAS模型,M-U-MIDAS模型普通最小二乘识别方法。并给出MIDAS模型OLS参数识别条件,同时将MIDAS预测模型正式引入回归模型的结构分析框架中,根据传统分布滞后模型参数含义给出了 MIDAS模型参数经济意义的理论依据,使MIDAS模型在不同频率变量之间进行结构分析成为可能。第五:证明了遗漏高频解释变量样本数据的非等权重部分将导致的偏误。分析了EQW模型(通过等权重平均将高频数据低频化后的传统回归模型)及MIDAS模型的内部结构,从理论上推导出了 EQW模型参数估计的偏误,MIDAS模型分离的线性与非线性两部分的参数预检验估计;在此基础上进一步讨论了混频数据回归模型与传统线性回归模型等价的约束条件,EQW模型估计量不存在偏误的条件,探索了 EQW模型估计量方差与MIDAS模型估计量方差之间的内在联系,MIDAS模型估计量及其方差的决定因素,推导了 MIDAS模型估计量的渐进分布等。通过严格的数学推导,最后发现,如果传统计量模型在建模之前只是简单的将高频变量数据通过平均低频化,遗漏了高频解释变量样本数据的非等权重部分将导致模型存在偏误,估计结果失真等后果;构建中国季度GDP五种不同权重函数的混频数据回归模型(MIDAS)和非限制性MIDAS,采用推导的OLS估计方法,对我国季度GDP进行了短期预报,分析了高频解释变量滞后阶数变化效应及其对低频变量GDP预测的影响效应;根据六种模型拟合及预测结果,进一步构建了混频回归联合预测模型,并考察了混频回归联合预测模型的预测精度及预测效果;研究结论表明,非限制性MIDAS模型的预测精度及拟合效果高于五种不同权重混频数据回归预测模型,采用BIC构建的非限制性混频回归联合预测模型在对我国季度GDP短期预测时表现最优。总之,本论文系统剖析了混频回归预测MIDAS模型的建模机制,内部结构,模型识别方法,参数的检验方法,与传统同频率回归模型的内在联系及其在实际经济的具体应用等。
[Abstract]:The traditional econometric model in the analysis of the representation of time series data variables, whether it is to build a model or specific application process are implied an important assumption, namely variables selected sample data must have the same frequency, otherwise the model cannot be identified, the traditional econometric model of non consistent frequency based data index data with the same frequency the requirements and practice will often make researchers into a situation in a nice hobble in the financial market, especially, combining micro and macro economics today, policymakers and researchers need to be a model in the case of less loss of effective information to the high frequency of macroeconomic data, ultra high frequency and low frequency of macro financial data economic data bridging, formal application in the traditional theory of this model in the actual economic bottlenecks, different frequency time series data with each passing day Under the background, mixing data econometric model analysis technology and the importance of increasingly prominent. In order to better introduce the development, modeling theory mixing data model, analysis technology and application fields, this paper deeply analyzes the regression model of mixing data (MIDAS) of the internal structure, and with the traditional distributed lag model for comparative analysis. Pointed out the difference between MIDAS model and traditional regression model, on the basis of combing the various MIDAS models of different forms, a variety of different forms of weighting function; numerical optimal algorithm is given to the mechanism of MIDAS model commonly used nonlinear least square and maximum likelihood estimation method and the deduction process; then on the basis of traditional recognition methods of distribution lag model, combined with the Vandermonde matrix is derived for the new estimation method of MIDAS model (ordinary least squares), are mixed The theoretical basis of frequency parameters of the model meaning, practical significance of the weight function, and the model is applied in the actual economic analysis in MIDAS class. In MIDAS model application, due to the choice of weighting function for the MIDAS model in this paper is crucial, overcomes the shortcomings of single weight function on the research study only selects MIDAS model, comprehensive consideration five different weight function form, and constructs the MIDAS model and the unrestricted MIDAS model in China were studied with different frequency index, there is considerable controversy in the economic field, at the same time with the traditional econometric model to do comparative analysis. Including the following parts: First: according to the data originally proposed prediction model of mixing the setting principle, combined with the traditional time series regression model derived from the basic form of model data and expand the form of mixing; including a mixed frequency data back Regression analysis, multivariate regression model of mixing data, multivariate autoregressive mixing data model, non limiting mixing data model, data mixing factor regression model, mixing data error correction model, mixing data Markov regime switching model, mixing vector autoregressive model. It is pointed out that the design thought, weight function summary, carding a variety of weight function the specific form, and to analyze the nature and the practical conditions of each weight function, on this basis, according to the Beta density function of a new weight function design. Second: the internal mechanism of commonly used estimation method of MIDAS model, are derived based on the nonlinear least squares NLS method MIDAS model, given the initial value, according to the specific form the target function of MIDAS model, the iterative formula of parameter estimation, by limiting the termination conditions to find convergence solutions, according to the nature of the objective function are discussed The objective function is to minimize the unconstrained conditions, numerical optimization algorithm combined with NLS, including the Newton method, Gauss Newton method, quasi Newton method, and the applicable conditions of these methods were pointed out, the operation efficiency and the advantages and disadvantages. The NLS estimation method, according to the index number according to the time attribute, which contains data on. Monthly data and quarterly data of six multivariate mixing regression model, analyzes the high-frequency asset price volatility and macro economy in China growth, inflation. The relationship between the first ring effect and path of economic growth in high frequency analysis of asset prices, comparative analysis of prediction results show: Exp Almon-AR-M-MIDAS model Almon index data the weight function constructed to extract more high-frequency variables on stock price, the fitting effect and prediction accuracy of sample optimal performance, the empirical results show that: high frequency Asset prices have significant effect on the impact of China's economic growth, and there are two kinds of alternate paths, to the early warning effect on economic growth. The effect of real estate price than the stock price, the stock price impact on the direction of economic instability. There followed in the analysis of high-frequency stock price variables on inflation the mechanism and prediction results, the empirical results show that: five the rapid decline of different weight functions in Beta- weight function whether it is fitting effect but also the forecast accuracy has a comparative advantage, timeliness and accuracy of the mixing data based on regression model has higher forecast in monthly inflation China, high asset prices of stock price significant effects on China's inflation, with the increase of the number of lags influence the stock price on inflation is fast Speed decreased. The prediction of traditional econometric models with the same frequency is better than the other and mixing data model. Third: given maximum likelihood estimation method of MIDAS model, the identification principle and specific process; combined with the specific form of the traditional maximum likelihood estimation and MIDAS model MIDAS-ML estimation and its asymptotic distribution is derived, and gives the MIDAS-ML estimators of variance covariance matrix simplified form is derived according to the pre test estimate method of statistical test set the parameters of the MIDAS model. By using this estimation method, the construction of six MIDAS the effects of monetary policy transmission mechanism and effectiveness of monetary policy effect on the economic growth and transfer path, the empirical results show that: the money supply as the representative of the monetary policy significantly affect economic growth in the short term, expansionary monetary policy to stimulate economic growth, in the long term, especially for 26 months to 37 months, Monetary policy on economic growth again play a role. Fourth: combining with the traditional estimation methods of distributed lag model, according to the internal mechanism of the MIDAS model, derived from the MIDAS model, M-MIDAS model, U-MIDAS model, M-U-MIDAS model and ordinary least squares identification method. The MIDAS model gives the OLS parameter identification conditions, while the structure of MIDAS model formally the regression model analysis framework, based on the traditional distributed lag model parameters gives the theoretical basis for the parameters of MIDAS model of economic significance, make the MIDAS model to analyze the structure become possible at different frequencies between variables. Fifth: proof of the missing high-frequency variables explain the non sample data weights will cause error analysis. The EQW model (by weight average of the traditional regression model of high frequency data and low frequency after) the internal structure and the MIDAS model, theoretically. Derived the error estimate the parameters of the EQW model, MIDAS model of separation of linear and nonlinear parameters of the two part on the basis of preliminary test estimation; further discusses the constraints of mixing data regression model with the traditional linear regression model is equivalent to the EQW estimator does not exist bias conditions, explore the EQW model estimation variance with the MIDAS model to estimate the relationship between the amount of variance, MIDAS model to estimate the determinants and variance, deduced the MIDAS model to estimate the amount of asymptotic distribution. Through strict mathematical derivation, and finally found that if the traditional econometric model before modeling simply to high frequency data from the average of the frequency, the omission of high frequency interpretation non variable data weight will cause the model errors, the estimation results distortion effect; construction China quarter GDP five different weight function The regression model mixing data (MIDAS) and non restrictive MIDAS estimation method using the deduced OLS, on China's quarterly GDP were short-term prediction analysis of high frequency variables lag order change effect and its influence on low frequency prediction variable GDP; according to the six kinds of model fitting and prediction results, further build mixing regression prediction model, and the prediction precision and the effect of mixing regression prediction model; the conclusion of the study shows that the prediction accuracy and the fitting effect of non restrictive MIDAS model is higher than that of five different weights according to the number of mixing regression prediction model, the non restrictive mixing BIC build regression joint forecast model in China Quarterly GDP short-term forecasting optimal performance. In short, this paper analyzes the mechanism of system modeling, mixing regression prediction MIDAS model structure, model identification, parameter test method, The internal relationship with the traditional same frequency regression model and its specific application in the actual economy.

【学位授予单位】：东北财经大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224

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