我国私人汽车拥有量分析.doc

1、我国私人汽车拥有量分析小组成 员: 黎桥(40204090) 部迪 (40204063)尹莉(40204259) 张凌放(40204157)于兰(40204034) 刘庆庆(40204268)董浩萍（40204032）前言：国家统计局最新公布的数据显示，国内大城市的私家车拥有量继续保持大幅增长的趋势。截止到年底，在全国十大城市的私家车拥有量排名中，北京私家车的拥有量以多出第二名近万辆的绝对优势排在了第一位。这十个城市的具体排名分别是：有关统计资料表明，我国城镇居民中有 3800 万户（占城镇居民总户数的24.8） ，有能力承受 10 万元左右的汽车消费。从近几年我国汽车消费的发展变化来看，汽车

2、消费将成为消费热点。从 1990 年到 2000 年的 10 年间，我国民用汽车的保有量由 551.36 万辆增加到 1608.91 万辆，平均每年增长 11.3。其中私人汽车拥有量由 1990 年的81.62 万辆增加到 2000 年的 625.73 万辆，平均每年增长 22.6。私人汽车拥有量占民用汽车的保有量比重从 1990 年的 14.8，上升到 2000 年的 38.9，平均每年上升 2.4 个百分点。1996 年以来，民用汽车拥有量的增加量中，私人汽车增加量的比重均高于 57.7，其中最高的是 1999 年，私人汽车增加量占全部民用汽车增加量的 82.5。这说明我国汽车市场结构发生

3、了根本性的变化，居民个人已经成为我国汽车市场的消费主体。随着我国经济突飞猛进的发展，人民群众的收入水平不断提高，特别是城镇居民的收入不断提高，私人汽车拥有量不断增加，同时银行的按揭贷款买车等等的一系列推动措施，也促进了私人汽车拥有俩的增加。单从经济方面来说，私人汽车拥有数量是评判一个国家人民生活水平的重要指标，对它的研究分析是有比较现实的意义的。我国私人汽车拥有量随时间变化图如下：数据收集：Y:我国私人汽车拥有量X1：城镇居民可支配收入X2：贷款利率X3：燃料、动力类价格指数（以 1990 年价格为的定比指数序列）具体数据如下:obs Y X1 X2（） X31990 816200 1510.

4、2 9.72 1001991 960400 1700.6 8.64 101.98741992 1182000 2026.6 8.64 118.71331993 1557700 2577.4 10.17 162.28111994 2054200 3496.2 10.98 191.49161995 2499600 4283 11.52 208.15141996 2896700 4838.9 10.53 229.38291997 3583600 5160.3 8.64 250.71551998 4236500 5425.1 7.08 248.4591999 5338800 5854 5.85 250

5、.69522000 6253300 6280 5.85 289.30222001 7707800 6859.6 5.85 289.88082002 9689800 7702.8 5.31 290.17072003 12192300 8472.2 5.31 311.6433普通的多元线性方程形式：Y 0+ 1x1+ 2x2+ 3x3先对各个变量做平稳性检验:对 YADF Test Statistic 1.082163 1% Critical Value* -4.32605% Critical Value -3.219510% Critical Value -2.7557*MacKinnon cr

6、itical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFY)Method: Least SquaresDate: 06/14/05 Time: 09:21Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariable Coefficient Std. Error t-Statistic Prob. ADFY

7、(-1) 0.334153 0.308782 1.082163 0.3286D(ADFY(-1) -0.121060 0.697271 -0.173620 0.8690D(ADFY(-2) -0.054606 0.945213 -0.057772 0.9562D(ADFY(-3) -0.409407 0.879632 -0.465430 0.6612C -105122.5 168342.6 -0.624456 0.5597R-squared 0.948366 Mean dependent var 1063460.Adjusted R-squared 0.907058 S.D. dependen

8、t var 710945.9S.E. of regression 216741.3 Akaike info criterion 27.71765Sum squared resid 2.35E+11 Schwarz criterion 27.86894Log likelihood -133.5882 F-statistic 22.95874Durbin-Watson stat 2.080638 Prob(F-statistic) 0.002042对 X1ADF Test Statistic -0.158912 1% Critical Value* -4.32605% Critical Value

9、 -3.219510% Critical Value -2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFX1)Method: Least SquaresDate: 06/14/05 Time: 09:26Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariab

10、le Coefficient Std. Error t-Statistic Prob. ADFX1(-1) -0.005477 0.034465 -0.158912 0.8800D(ADFX1(-1) 0.664445 0.406596 1.634162 0.1632D(ADFX1(-2) -0.331605 0.522131 -0.635100 0.5533D(ADFX1(-3) -0.414658 0.416042 -0.996674 0.3647C 609.9278 275.2910 2.215575 0.0776R-squared 0.746497 Mean dependent var

11、 589.4800Adjusted R-squared 0.543694 S.D. dependent var 229.7711S.E. of regression 155.2114 Akaike info criterion 13.23431Sum squared resid 120452.9 Schwarz criterion 13.38560Log likelihood -61.17153 F-statistic 3.680899Durbin-Watson stat 2.031160 Prob(F-statistic) 0.092741对 X2ADF Test Statistic -0.

12、529198 1% Critical Value* -4.32605% Critical Value -3.219510% Critical Value -2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFX2)Method: Least SquaresDate: 06/14/05 Time: 09:27Sample(adjusted): 1994 2003Include

13、d observations: 10 after adjusting endpointsVariable Coefficient Std. Error t-Statistic Prob. ADFX2(-1) -0.069982 0.132242 -0.529198 0.6193D(ADFX2(-1) 0.543426 0.321159 1.692075 0.1514D(ADFX2(-2) 0.140535 0.368364 0.381510 0.7185D(ADFX2(-3) -0.391387 0.347038 -1.127794 0.3106C 0.155018 1.219842 0.12

14、7080 0.9038R-squared 0.768917 Mean dependent var -0.486000Adjusted R-squared 0.584050 S.D. dependent var 0.905296S.E. of regression 0.583863 Akaike info criterion 2.068551Sum squared resid 1.704478 Schwarz criterion 2.219843Log likelihood -5.342754 F-statistic 4.159310Durbin-Watson stat 2.443814 Pro

15、b(F-statistic) 0.075014对 X3ADF Test Statistic -2.501558 1% Critical Value* -4.32605% Critical Value -3.219510% Critical Value -2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFX3)Method: Least SquaresDate: 06/14

16、/05 Time: 09:27Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariable Coefficient Std. Error t-Statistic Prob. ADFX3(-1) -0.296326 0.118457 -2.501558 0.0544D(ADFX3(-1) -0.332083 0.323046 -1.027973 0.3511D(ADFX3(-2) -0.592595 0.256861 -2.307066 0.0692D(ADFX3(-3) 0.0791

17、95 0.290428 0.272684 0.7960C 101.6956 38.34296 2.652262 0.0453R-squared 0.684768 Mean dependent var 14.93622Adjusted R-squared 0.432582 S.D. dependent var 14.01521S.E. of regression 10.55726 Akaike info criterion 7.858358Sum squared resid 557.2788 Schwarz criterion 8.009650Log likelihood -34.29179 F

18、-statistic 2.715332Durbin-Watson stat 1.902782 Prob(F-statistic) 0.151305由此可见，各个变量的随时间变化是平稳的，可以对其直接进行最小二乘估计。对其作普通最小二乘估计：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 16:43Sample: 1990 2003Included observations: 14Variable Coefficient Std. Error t-Statistic Prob. C 3250054. 1725513.

19、1.883529 0.0890X1 2922.028 515.0624 5.673154 0.0002X2 -214742.9 155673.7 -1.379442 0.1978X3 -50492.48 14255.54 -3.541955 0.0053R-squared 0.964556 Mean dependent var4354921.Adjusted R-squared 0.953922 S.D. dependent var 3498430.S.E. of regression 750961.7 Akaike info criterion 30.13105Sum squared res

20、id 5.64E+12 Schwarz criterion 30.31364Log likelihood -206.9174 F-statistic 90.71108Durbin-Watson stat 1.514620 Prob(F-statistic) 0.000000样本回归模型为:y=3250054+2922.028x1-214742.9x2-50492.48x3(1725513) (515.0624) (155673.7) (14255.54)t=(1.883529) (5.673154) (-1.379442) (-3.541955)Adjusted R2-=0.953922 F=

21、90.71108经观察：各个系数符合经济意义;从可决系数看拟合优度较好;X2 的 T 检验不显著，而 F 统计量显著，效果很好，可以推断解释变量可能存在多重共线性。一、多重共线性的检验与修正：下面是 x1 x2 x3 的简单相关系数矩阵:x1 x2 x3x1 1 -0.73851 0.975673x2 -0.73851 1 -0.66181x3 0.975673 -0.66181 1可见,各个变量相关系数很高, x1 x3 尤为突出.我们采用逐步回归法进行修正：（1）运用 OLS 方法逐一求 Y 对各个解释变量的回归，结合经济意义和统计检验出拟合效果最好的一个一元线性回归方程：方程 1：Dep

22、endent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:08Sample: 1990 2003Included observations: 14Variable Coefficient Std. Error t-Statistic Prob. C -2616509. 787741.3 -3.321533 0.0061X1 1474.612 151.6332 9.724864 0.0000R-squared 0.887401 Mean dependent var 4354921.Adjusted R-squared 0.878

23、018 S.D. dependent var 3498430.S.E. of regression 1221860. Akaike info criterion 31.00121Sum squared resid 1.79E+13 Schwarz criterion 31.09250Log likelihood -215.0085 F-statistic 94.57299Durbin-Watson stat 0.273300 Prob(F-statistic) 0.000000方程 2：Dependent Variable: YMethod: Least SquaresDate: 06/03/

24、05 Time: 17:08Sample: 1990 2003Included observations: 14Variable Coefficient Std. Error t-Statistic Prob. C 15041904 2243778. 6.703828 0.0000X2 -1322763. 268920.1 -4.918796 0.0004R-squared 0.668458 Mean dependent var 4354921.Adjusted R-squared 0.640830 S.D. dependent var 3498430.S.E. of regression 2

25、096637. Akaike info criterion 32.08113Sum squared resid 5.28E+13 Schwarz criterion 32.17243Log likelihood -222.5679 F-statistic 24.19456Durbin-Watson stat 0.583287 Prob(F-statistic) 0.000355方程 3:Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:09Sample: 1990 2003Included observation

26、s: 14Variable Coefficient Std. Error t-Statistic Prob. C -4659138. 1615330. -2.884325 0.0137X3 41472.90 7074.333 5.862447 0.0001R-squared 0.741202 Mean dependent var 4354921.Adjusted R-squared 0.719636 S.D. dependent var 3498430.S.E. of regression 1852398. Akaike info criterion 31.83342Sum squared r

27、esid 4.12E+13 Schwarz criterion 31.92472Log likelihood -220.8340 F-statistic 34.36829Durbin-Watson stat 0.332537 Prob(F-statistic) 0.000077(2)对比分析，依据调整后可决系数最大原则，选取 X1 进入回归模型的第一个解释变量，形成一元回归模型:Y=-2616509+0.887401x1(787741.3) (151.6332)t=(-3.321533) (9.724864)Adjusted R-squared=0.878018 F=94.57299（3）逐步

28、回归，将其余变量分别加入模型：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:13Sample: 1990 2003Included observations: 14Variable Coefficient Std. Error t-Statistic Prob. C 2354107. 2443622. 0.963368 0.3561X1 1164.618 197.8825 5.885402 0.0001X2 -433834.9 204519.4 -2.121241 0.0574R-squared 0.9200

29、89 Mean dependent var 4354921.Adjusted R-squared 0.905560 S.D. dependent var 3498430.S.E. of regression 1075105. Akaike info criterion 30.80114Sum squared resid 1.27E+13 Schwarz criterion 30.93808Log likelihood -212.6080 F-statistic 63.32690Durbin-Watson stat 0.449924 Prob(F-statistic) 0.000001Depen

30、dent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:13Sample: 1990 2003Included observations: 14Variable Coefficient Std. Error t-Statistic Prob. C 1316764. 1047067. 1.257573 0.2346X1 3323.203 442.2023 7.515119 0.0000X3 -58306.16 13608.15 -4.284650 0.0013R-squared 0.957811 Mean dependent va

31、r 4354921.Adjusted R-squared 0.950141 S.D. dependent var 3498430.S.E. of regression 781172.8 Akaike info criterion 30.16239Sum squared resid 6.71E+12 Schwarz criterion 30.29933Log likelihood -208.1367 F-statistic 124.8664Durbin-Watson stat 1.457294 Prob(F-statistic) 0.000000由上表可以看出，X3 和 X1 构建的模型的拟合值

32、优于 X2 和 X1 构建的方程的拟合值，且比起 y 对 x1 的回归拟合优度更好,t 检验和 F 检验都更显著，所以在Y=-2616509+0.887401x1 的基础上加入解释变量 x3,得:Y=1316764+3323.203x1-58306.16x3(1047067) (442.2023) (13608.15)t=(1.257573) (7.515119) (-4.284665)Adjusted R-squared=0.950141 F=124.8664二、异方差的检验与修正因为时间序列数据，样本个数较小，所以选用 ARCH 检验：Dependent Variable: E2Metho

33、d: Least SquaresDate: 06/03/05 Time: 18:31Sample(adjusted): 1993 2003Included observations: 11 after adjusting endpointsVariable Coefficient Std. Error t-Statistic Prob. C 4.33E+11 1.37E+12 0.314942 0.7620E2(-1) 3.475572 0.832087 4.176932 0.0042E2(-2) -3.867453 1.376776 -2.809065 0.0262E2(-3) 1.4041

34、65 1.117624 1.256384 0.2493R-squared 0.827082 Mean dependent var 2.96E+12Adjusted R-squared 0.752974 S.D. dependent var 3.55E+12S.E. of regression 1.76E+12 Akaike info criterion 59.51134Sum squared resid 2.18E+25 Schwarz criterion 59.65603Log likelihood -323.3124 F-statistic 11.16052Durbin-Watson stat 1.980794 Prob(F-statistic) 0.004656计算(n-p) R2 = 6.616656临界值 7.81(=0.05),所以接受 Ho,表明模型中不存在异方差。三、自相关的检验和修正（1）下面是 e 与 e（-1）的坐标图：