本文關(guān)鍵詞： 混頻數(shù)據(jù) MIDAS類模型 估計方法 EQW模型 季度GDP 通貨膨脹 資產(chǎn)價格　出處：《東北財經(jīng)大學》2016年博士論文　論文類型：學位論文

【摘要】：傳統(tǒng)計量經(jīng)濟模型在分析時間序列數(shù)據(jù)所表示的變量時,無論是模型的構(gòu)建,還是具體應(yīng)用過程均暗含一個重要假定,即選取的變量樣本數(shù)據(jù)必須具有同頻率特性,否則模型無法識別,傳統(tǒng)計量經(jīng)濟模型對指標數(shù)據(jù)同頻率的要求及實際中基礎(chǔ)數(shù)據(jù)頻率的不一致性往往會使研究人員陷入進退兩難的境地,特別是在金融市場,微觀經(jīng)濟與宏觀經(jīng)濟緊密結(jié)合的今天,政策制定者和研究人員急需一種模型在少損失有效信息情況下能夠?qū)⒏哳l宏觀經(jīng)濟數(shù)據(jù)、超高頻金融數(shù)據(jù)與低頻宏觀經(jīng)濟數(shù)據(jù)橋接起來,正式在這種傳統(tǒng)理論模型應(yīng)用處于瓶頸,實際經(jīng)濟中不同頻率時間序列數(shù)據(jù)日新月異的背景下,混頻數(shù)據(jù)計量經(jīng)濟模型分析技術(shù)及重要性逐漸凸顯出來。為了更好的引進,發(fā)展混頻數(shù)據(jù)模型的建模理論,分析技術(shù)及應(yīng)用等領(lǐng)域的研究,本論文深入剖析了混頻數(shù)據(jù)回歸模型(MIDAS)的內(nèi)部結(jié)構(gòu),并與傳統(tǒng)分布滯后模型作對比分析,指出MIDAS模型與傳統(tǒng)回歸模型的區(qū)別與聯(lián)系,在此基礎(chǔ)上系統(tǒng)梳理了 MIDAS模型的各種不同形式,多種不同形式的權(quán)重函數(shù);結(jié)合數(shù)值化最優(yōu)算法給出了 MIDAS類模型常用非線性最小二乘及最大似然估計方法的具體機理及演繹過程;隨后依據(jù)傳統(tǒng)分布滯后模型的識別方法,結(jié)合范德蒙矩陣推導出了 MIDAS類模型的新估計方法(普通最小二乘法),給出了混頻模型參數(shù)含義的理論基礎(chǔ),權(quán)重函數(shù)的實際意義,并將MIDAS類模型應(yīng)用于實際經(jīng)濟分析中。在MIDAS類模型應(yīng)用方面,由于權(quán)重函數(shù)的選擇對于MIDAS模型至關(guān)重要,本論文克服了以往關(guān)于MIDAS模型研究中只選取單一權(quán)重函數(shù)的不足,全面考慮了五種不同權(quán)重函數(shù)形式,并以此構(gòu)建MIDAS類模型及非限制MIDAS類模型研究了我國具有不同頻率指標,存在較大爭議的經(jīng)濟領(lǐng)域中,同時與傳統(tǒng)計量經(jīng)濟模型做比較分析。具體包括以下幾個部分:第一:根據(jù)最初提出的混頻數(shù)據(jù)預(yù)測模型設(shè)置原理,結(jié)合傳統(tǒng)時間序列回歸模型推導出了混頻數(shù)據(jù)回歸模型的基本形式及拓展形式;主要包括一元混頻數(shù)據(jù)回歸模型,多元混頻數(shù)據(jù)回歸模型,自回歸多元混頻數(shù)據(jù)模型,非限制混頻數(shù)據(jù)回歸模型,混頻數(shù)據(jù)因子回歸模型、混頻數(shù)據(jù)誤差修正模型,混頻數(shù)據(jù)馬爾可夫區(qū)制轉(zhuǎn)移模型、混頻向量自回歸模型等。指出權(quán)重函數(shù)的設(shè)計思想,概括、梳理出多種權(quán)重函數(shù)具體形式,并剖析每種權(quán)重函數(shù)的性質(zhì)及實用條件,在此基礎(chǔ)上,根據(jù)Beta密度函數(shù)設(shè)計了新權(quán)重函數(shù)。第二:闡述了 MIDAS類模型常用估計方法的內(nèi)在機理,從理論上推導出了 MIDAS模型的非線性最小二乘NLS法,給定初始值,依據(jù)MIDAS模型目標函數(shù)的具體形式,導出參數(shù)估計的迭代公式,通過限定終止條件找到收斂解,根據(jù)目標函數(shù)的性質(zhì),主要討論目標函數(shù)為無約束條件的極小化,與NLS結(jié)合的數(shù)值最優(yōu)化算法,包括牛頓法,高斯牛頓法,擬牛頓法等,同時指出了這些方法的適用條件,運算效率及優(yōu)缺點。采用上述NLS估計方法,根據(jù)指標數(shù)據(jù)時間屬性,構(gòu)建了包含日數(shù)據(jù),月度數(shù)據(jù)及季度數(shù)據(jù)的六種多元混頻數(shù)據(jù)回歸模型,分析了我國高頻資產(chǎn)價格波動與宏觀經(jīng)濟增長、通貨膨脹的關(guān)系。首先在分析高頻資產(chǎn)價格對經(jīng)濟增長的影響效應(yīng)及作用路徑時,預(yù)測結(jié)果的對比分析顯示:基于Almon指數(shù)權(quán)重函數(shù)構(gòu)建的Exp Almon-AR-M-MIDAS模型能夠提取更多高頻變量股票價格的日數(shù)據(jù)信息,其擬合效果及樣本內(nèi)預(yù)測精度表現(xiàn)最優(yōu),實證結(jié)果表明:高頻資產(chǎn)價格對我國經(jīng)濟增長的影響效應(yīng)顯著,并且存在正負交替兩種作用路徑,能夠?qū)?jīng)濟增長起到提前預(yù)警作用。其中房地產(chǎn)價格的影響效應(yīng)大于股票價格,股票價格對經(jīng)濟的影響方向存在不穩(wěn)定性。其次在分析高頻變量股票價格對通貨膨脹的作用機制及預(yù)測效果時,實證結(jié)果表明:五種不同權(quán)重函數(shù)中快速下降的Beta-權(quán)重函數(shù)無論是擬合效果還是預(yù)測精度上都具有比較優(yōu)勢,以此構(gòu)建的混頻數(shù)據(jù)回歸模型在中國通貨膨脹的月度預(yù)報方面具有較高的時效性和精確性,高頻資產(chǎn)價格股票價格對我國通貨膨脹影響效應(yīng)顯著,隨著滯后階數(shù)的增加股票價格對通貨膨脹的影響程度呈迅速下降趨勢。其預(yù)測效果優(yōu)于同頻率的傳統(tǒng)計量模型和其他混頻數(shù)據(jù)模型。第三:給出了MIDAS模型極大似然估計方法,識別原理及具體過程;結(jié)合傳統(tǒng)極大似然估計和MIDAS模型具體形式系統(tǒng)推導了 MIDAS-ML估計量及其漸進分布,并給出MIDAS-ML估計量方差協(xié)方差矩陣簡化形式,根據(jù)推導預(yù)檢驗估計量設(shè)置MIDAS模型參數(shù)的統(tǒng)計檢驗方法。采用此估計方法,構(gòu)建六種MIDAS考察了貨幣政策的傳導機制及有效性,貨幣政策對經(jīng)濟增長的影響效果和傳遞路徑,實證結(jié)果表明:以貨幣供應(yīng)量為代表的貨幣政策顯著影響經(jīng)濟增長,短期內(nèi),擴張的貨幣政策能夠拉動經(jīng)濟增長,長期內(nèi),特別是26個月直至37個月,貨幣政策對經(jīng)濟增長再次發(fā)揮出促進作用。第四:結(jié)合傳統(tǒng)分布滯后模型的估計方法,根據(jù)MIDAS模型的內(nèi)在機理,推導出了 MIDAS模型,M-MIDAS模型,U-MIDAS模型,M-U-MIDAS模型普通最小二乘識別方法。并給出MIDAS模型OLS參數(shù)識別條件,同時將MIDAS預(yù)測模型正式引入回歸模型的結(jié)構(gòu)分析框架中,根據(jù)傳統(tǒng)分布滯后模型參數(shù)含義給出了 MIDAS模型參數(shù)經(jīng)濟意義的理論依據(jù),使MIDAS模型在不同頻率變量之間進行結(jié)構(gòu)分析成為可能。第五:證明了遺漏高頻解釋變量樣本數(shù)據(jù)的非等權(quán)重部分將導致的偏誤。分析了EQW模型(通過等權(quán)重平均將高頻數(shù)據(jù)低頻化后的傳統(tǒng)回歸模型)及MIDAS模型的內(nèi)部結(jié)構(gòu),從理論上推導出了 EQW模型參數(shù)估計的偏誤,MIDAS模型分離的線性與非線性兩部分的參數(shù)預(yù)檢驗估計;在此基礎(chǔ)上進一步討論了混頻數(shù)據(jù)回歸模型與傳統(tǒng)線性回歸模型等價的約束條件,EQW模型估計量不存在偏誤的條件,探索了 EQW模型估計量方差與MIDAS模型估計量方差之間的內(nèi)在聯(lián)系,MIDAS模型估計量及其方差的決定因素,推導了 MIDAS模型估計量的漸進分布等。通過嚴格的數(shù)學推導,最后發(fā)現(xiàn),如果傳統(tǒng)計量模型在建模之前只是簡單的將高頻變量數(shù)據(jù)通過平均低頻化,遺漏了高頻解釋變量樣本數(shù)據(jù)的非等權(quán)重部分將導致模型存在偏誤,估計結(jié)果失真等后果;構(gòu)建中國季度GDP五種不同權(quán)重函數(shù)的混頻數(shù)據(jù)回歸模型(MIDAS)和非限制性MIDAS,采用推導的OLS估計方法,對我國季度GDP進行了短期預(yù)報,分析了高頻解釋變量滯后階數(shù)變化效應(yīng)及其對低頻變量GDP預(yù)測的影響效應(yīng);根據(jù)六種模型擬合及預(yù)測結(jié)果,進一步構(gòu)建了混頻回歸聯(lián)合預(yù)測模型,并考察了混頻回歸聯(lián)合預(yù)測模型的預(yù)測精度及預(yù)測效果;研究結(jié)論表明,非限制性MIDAS模型的預(yù)測精度及擬合效果高于五種不同權(quán)重混頻數(shù)據(jù)回歸預(yù)測模型,采用BIC構(gòu)建的非限制性混頻回歸聯(lián)合預(yù)測模型在對我國季度GDP短期預(yù)測時表現(xiàn)最優(yōu)�？傊�,本論文系統(tǒng)剖析了混頻回歸預(yù)測MIDAS模型的建模機制,內(nèi)部結(jié)構(gòu),模型識別方法,參數(shù)的檢驗方法,與傳統(tǒng)同頻率回歸模型的內(nèi)在聯(lián)系及其在實際經(jīng)濟的具體應(yīng)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.

【學位授予單位】：東北財經(jīng)大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：F224

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