本文選題：線性自回歸 + 半?yún)?shù)自回歸��； 參考：《河南科技大學(xué)》2013年碩士論文

【摘要】：合理預(yù)測(cè)“十二五”時(shí)期河南省經(jīng)濟(jì)發(fā)展趨勢(shì)和狀況，為省委、省政府和有關(guān)部門進(jìn)行科學(xué)決策和有效管理提供定量依據(jù)，對(duì)促進(jìn)中原經(jīng)濟(jì)區(qū)建設(shè)具有重要的現(xiàn)實(shí)意義。 半?yún)?shù)回歸模型既含有參數(shù)分量又含有非參數(shù)分量，它不但保留了參數(shù)模型易于解釋的優(yōu)點(diǎn)，，而且還具有建模的靈活性。本文基于半?yún)?shù)回歸理論與方法建立了河南省國(guó)內(nèi)生產(chǎn)總值(GDP)指數(shù)、人均GDP指數(shù)及第一、二、三產(chǎn)業(yè)指數(shù)(1952年為100)的半?yún)?shù)自回歸模型，并且對(duì)相關(guān)經(jīng)濟(jì)指標(biāo)進(jìn)行了預(yù)測(cè)分析，具體內(nèi)容如下： 1．詳細(xì)給出了河南省GDP指數(shù)的線性自回歸建模過(guò)程，以線性自回歸模型的顯著變量為半?yún)?shù)模型的線性主部變量、非顯著變量為非參數(shù)函數(shù)變量，采用多項(xiàng)式樣條估計(jì)方法建立了GDP指數(shù)的半?yún)?shù)趨勢(shì)自回歸模型。該模型對(duì)1985-2010年GDP指數(shù)擬合的均方標(biāo)準(zhǔn)誤差(RMSE)為61.45，平均絕對(duì)百分誤差(MAPE)為1.14%，預(yù)測(cè)結(jié)果表明：“十二五”時(shí)期，河南省GDP指數(shù)年均增長(zhǎng)速度為9.26%，仍然呈現(xiàn)著較為平穩(wěn)的發(fā)展態(tài)勢(shì)。 2．類似于GDP指數(shù)的建模方法，建立了人均GDP指數(shù)的半?yún)?shù)自回歸模型，其中滯后一、三、四、六階變量為線性主部變量，滯后五階變量為非參數(shù)函數(shù)變量。該模型對(duì)1985-2010年人均GDP指數(shù)擬合的RMSE為40.28，MAPE為1.30%。預(yù)測(cè)結(jié)果表明：“十二五”時(shí)期人均GDP指數(shù)仍將穩(wěn)步增長(zhǎng)，年均增速為9.35%，到2015年，人均GDP指數(shù)將超過(guò)6500。 3．采用GDP指數(shù)的建模方法，建立了河南省第一產(chǎn)業(yè)指數(shù)的半?yún)?shù)自回歸模型。該模型對(duì)1984-2010年第一產(chǎn)業(yè)擬合的RMSE為19.45，MAPE為2.94%，且2011-2015年第一產(chǎn)業(yè)指數(shù)值分別為1111.1，1174.0，1221.5，1285.8，1347.4，其中對(duì)2011年的預(yù)測(cè)誤差僅為0.32%，整個(gè)“十二五”時(shí)期第一產(chǎn)業(yè)指數(shù)的年均增速為4.61%。 4．基于多項(xiàng)式樣條估計(jì)理論，對(duì)河南省第二產(chǎn)業(yè)指數(shù)建立了具有外生變量的半?yún)?shù)自回歸模型，其中第二產(chǎn)業(yè)和第三產(chǎn)業(yè)的顯著性滯后變量作為線性部分，第一產(chǎn)業(yè)作為非參數(shù)部分。該模型對(duì)1980-2010年第二產(chǎn)業(yè)指數(shù)擬合的RMSE為439.69，MAPE為3.5%。預(yù)測(cè)結(jié)果顯示：“十二五”時(shí)期河南省第二產(chǎn)業(yè)指數(shù)由2011年的71683.4迅速增加到2015年的111376.9，年均增速為11.92%。 5．通過(guò)構(gòu)建河南省第三產(chǎn)業(yè)指數(shù)的線性自回歸模型，將非顯著一階滯后變量作為非參數(shù)函數(shù)變量，基于多項(xiàng)式樣條方法建立了第三產(chǎn)業(yè)指數(shù)的半?yún)?shù)自回歸模型。通過(guò)計(jì)算，所建立的半?yún)?shù)模型對(duì)1981-2010年第三產(chǎn)業(yè)指數(shù)擬合的RMSE為203.36，MAPE為2.49%，且“十二五”時(shí)期第三產(chǎn)業(yè)指數(shù)的年均增速為10.93%，除了2012年的環(huán)比增速為9.15%，其它年份環(huán)比增速都將超過(guò)10%。 總之，“十二五”時(shí)期，河南省經(jīng)濟(jì)仍將呈現(xiàn)較為平穩(wěn)的增長(zhǎng)態(tài)勢(shì)，人均GDP指數(shù)及三大產(chǎn)業(yè)指數(shù)也將穩(wěn)步提高，其中第二產(chǎn)業(yè)在河南產(chǎn)業(yè)結(jié)構(gòu)中仍居主導(dǎo)地位，第三產(chǎn)業(yè)也將得到較快的發(fā)展。
[Abstract]:Reasonable prediction of the economic development trend and situation in Henan Province during the 12th Five-Year Plan period provides quantitative basis for scientific decision-making and effective management of provincial party committee, provincial government and relevant departments, and has important practical significance for promoting the construction of Central Plains Economic Zone. The semi-parametric regression model contains both parametric and non-parametric components. It not only retains the advantages of the parametric model which is easy to interpret, but also has the flexibility of modeling. Based on the semi-parametric regression theory and method, this paper establishes a semi-parametric autoregressive model of Henan's gross domestic product (GDP) index, per capita GDP index and the index of first, second and third industries (100 in 1952). The details are as follows: 1. The linear autoregressive modeling process of GDP exponent in Henan Province is given in detail. The significant variable of the linear autoregressive model is the linear principal variable of the semi-parametric model, and the non-significant variable is the non-parametric functional variable. The semiparametric trend autoregressive model of GDP exponent is established by using polynomial spline estimation method. From 1985 to 2010, the mean square standard error (RMSE) of GDP index fitting is 61.45, and the average absolute percent error is 1.14. The forecast results show that the average annual growth rate of GDP index in Henan Province is 9.26 during the 12th Five-Year Plan period, which still presents a steady development trend. 2. Similar to the modeling method of GDP exponent, the semi-parametric autoregressive model of per capita GDP exponent is established, in which the variables of order 1, 3, 4 and 6 are linear principal variables, and the variables of order 5 lag are nonparametric functional variables. The RMSE of the model fitted to the per capita GDP index from 1985 to 2010 is 40.28 and 1.30. The forecast results show that the per capita GDP index will continue to grow steadily during the 12th Five-Year Plan period, with an average annual growth rate of 9.35. By 2015, the per capita GDP index will exceed 6500. 3. The semi-parametric autoregressive model of primary industry index in Henan Province is established by using GDP index modeling method. The RMSE of this model for the primary industry from 1984 to 2010 is 19.45% and 2.94 respectively, and the primary industry index values for 2011-2015 are 1111.1 / 1174.01221.5/ 1285.81347.4 respectively. The forecast error for 2011 is only 0.32, and the average annual growth rate of the first industry index is 4.61in the whole "12th Five-Year Plan" period. 4. Based on polynomial spline estimation theory, a semi-parametric autoregressive model with exogenous variables is established for the secondary industry index in Henan Province, in which the significant lag variables of the secondary industry and the tertiary industry are regarded as the linear part. Primary industry as a non-parametric part. The RMSE of the model fitting the secondary industry index from 1980 to 2010 is 439.69 and 3.5. The forecast results show that the secondary industry index of Henan Province increased rapidly from 71683.4 in 2011 to 111,1376.9 in 2015, with an average annual growth rate of 11.92 in the 12th Five-Year Plan period. 5. By constructing the linear autoregressive model of the tertiary industry index in Henan Province, the semi-parametric autoregressive model of the tertiary industry index is established based on the polynomial spline method, which takes the non-significant first-order lag variable as the non-parametric function variable. Through the calculation, the RMSE of the semi-parametric model fitting the tertiary industry index from 1981 to 2010 is 203.36 MAPE is 2.49, and the average annual growth rate of the tertiary industry index in the 12th Five-Year Plan period is 10.933. Except for the 9.15 percent growth rate in 2012, the other year's growth rate will exceed 10 percent. In a word, during the 12th Five-Year Plan period, Henan's economy will still present a relatively stable growth trend, and the per capita GDP index and the three major industrial indices will also steadily increase, and the secondary industry will still occupy a dominant position in Henan's industrial structure. The tertiary industry will also get faster development.
【學(xué)位授予單位】：河南科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F127;F224

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