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?2量n偏小（21<25,50,100
?2）。根据公式
Cp?????1/T??2/TCp?????1/T??2/T以及表中数据求得5%先著水平下t检验临
界值为-4.660579，小于5%的时的临界值。因此这四个变量间存在协整关系。可以用传统的计量方法进行回归分析。
下面用传统的回归方法进行检验：
1、多重共线性检验
对CPI GDP R X 进行多重共线性检验得到表6 表6
Dependent Variable: CPI Method: Least Squares Date: 12/15/07 Time: 09:49 Sample: 1985 2005 Included observations: 21
CoefficienVariable t Std. Error t-Statistic
C 55.15753 52.19991 1.056660 GDP 0.367925 0.051004 7.213656 R 31.38562 16.74099 1.874777 X -7.973643 1.905748 -4.183996 R-squared 0.889257 Mean dependent var
Adjusted R-squared 0.869714 S.D. dependent var S.E. of regression 34.31605 Akaike info criterion Sum squared resid 20019.05 Schwarz criterion Log likelihood -101.8268 F-statistic Durbin-Watson stat 0.966201 Prob(F-statistic)
可以得到模型的估计结果：
CPI=55.1573+0.367925GDP+31.38562R-7.973643X (52.19991) ( 0.051004) ( 16.74099) ( 1.905748)
t=(1.056660)( 7.213656) ( 1.874777) ( -4.183996)
2 Prob. 0.3055 0.0000 0.0781 0.0006 250.9286 95.07114 10.07875 10.27770 45.50288 0.000000
R2=0.889257 R=0.869714 F=45.50288 df=17
从上述回归结果看，在数据为时间序列时，可决系数较高，拟合优度较好（R0.889257接近于
0.9）。在10%的显著水平下，查F分布表得?F?(3,17)=2.44。可以看出F>F?且相应的p=0.000000。整体效果的F检验通过。说明回归方程显著。但是利率R的t检验不显著，且相应的p=0.0781，说明R对CPI影响不显著。可能存在程度较小的多重共线性。下面进行判断：
GDP、R、X的简单相关系数矩阵如表7
2=
表7
GDP R X
GDP 1.000000 -0.858279 0.334253
R -0.858279 1.000000 -0.115687
X 0.334253 -0.115687 1.000000
由表7可以看出：GDP和R之间相关系数绝对值较高，GDP和R之间高度相关，证实解释变量之间存在多重共线性。为了消除多重共线性对模型的影响，我们采用逐步回归法进行修正。
分别对解释变量做一元回归得表8、表9、表10
表8
Dependent Variable: CPI Method: Least Squares Date: 12/15/07 Time: 11:05 Sample: 1985 2005 Included observations: 21
CoefficienVariable t Std. Error t-Statistic
C 125.9624 18.50048 6.808601 GDP 0.253200 0.031383 8.068120 R-squared 0.774064 Mean dependent var
Adjusted R-squared 0.762172 S.D. dependent var S.E. of regression 46.36388 Akaike info criterion Sum squared resid 40842.57 Schwarz criterion Log likelihood -109.3138 F-statistic Durbin-Watson stat 0.147370 Prob(F-statistic) 表9
Dependent Variable: CPI Method: Least Squares Date: 12/15/07 Time: 11:06 Sample: 1985 2005 Included observations: 21
CoefficienVariable t Std. Error t-Statistic
C 390.4610 32.63223 11.96550 R -73.43814 15.41975 -4.762601 R-squared 0.544172 Mean dependent var
Adjusted R-squared 0.520181 S.D. dependent var S.E. of regression 65.85481 Akaike info criterion
Prob. 0.0000 0.0000 250.9286 95.07114 10.60131 10.70079 65.09456 0.000000
Prob. 0.0000 0.0001 250.9286 95.07114 11.30317
Sum squared resid Log likelihood
Durbin-Watson stat 82400.25 Schwarz criterion -116.6833 F-statistic
0.326543 Prob(F-statistic) 11.40265 22.68237 0.000135
表10
Dependent Variable: CPI Method: Least Squares Date: 12/15/07 Time: 11:06 Sample: 1985 2005 Included observations: 21
CoefficienVariable t Std. Error t-Statistic
C 250.0093 34.55058 7.236037 X 0.161275 4.774739 0.033777 R-squared 0.000060 Mean dependent var
Adjusted R-squared -0.052568 S.D. dependent var S.E. of regression 97.53800 Akaike info criterion Sum squared resid 180759.6 Schwarz criterion Log likelihood -124.9319 F-statistic Durbin-Watson stat 0.041737 Prob(F-statistic)
2 Prob. 0.0000 0.9734 250.9286 95.07114 12.08875 12.18823 0.001141 0.973408
由表8、表9、表10进行对比分析，依据调整后R最大的原则，选取GDP作为进入回归模型的第一个变量，形成一元回归。然后进行逐步回归，得到表11、表12
表11
Dependent Variable: CPI Method: Least Squares Date: 12/15/07 Time: 12:03 Sample: 1985 2005 Included observations: 21
CoefficienVariable t Std. Error t-Statistic
C 105.3614 70.33827 1.497924 GDP 0.269559 0.062668 4.301370 R 6.593259 21.67829 0.304141 R-squared 0.775219 Mean dependent var
Adjusted R-squared 0.750243 S.D. dependent var S.E. of regression 47.51243 Akaike info criterion Sum squared resid 40633.76 Schwarz criterion
Prob. 0.1515 0.0004 0.7645 250.9286 95.07114 10.69142 10.84064
表12
Dependent Variable: CPI Method: Least Squares Date: 12/15/07 Time: 12:03 Sample: 1985 2005 Included observations: 21
CoefficienVariable t Std. Error t-Statistic
C 148.9000 16.00057 9.305922 GDP 0.284208 0.026311 10.80198 X -6.709022 1.902815 -3.525840 R-squared 0.866361 Mean dependent var
Adjusted R-squared 0.851512 S.D. dependent var S.E. of regression 36.63486 Akaike info criterion Sum squared resid 24158.03 Schwarz criterion Log likelihood -103.8001 F-statistic Durbin-Watson stat 0.611067 Prob(F-statistic)
2Log likelihood
Durbin-Watson stat
-109.2599 F-statistic
0.142459 Prob(F-statistic)
31.03897
0.000001
Prob. 0.0000 0.0000 0.0024 250.9286 95.07114 10.17144 10.32066 58.34546 0.000000
对比表11和表12的结果，并根据逐步回归思想，可以得到：新加入变量X的二元回归方程
R=0.851512最大，并且各个参数t检验显著，且参数符号也符合经济意义。进一步进行逐步
回归得到表13
表13
Dependent Variable: CPI Method: Least Squares
Date: 12/15/07 Time: 12:17 Sample: 1985 2005
Included observations: 21
CoefficienVariable t
C 55.15753 GDP 0.367925 X -7.973643 R 31.38562
Std. Error 52.19991 0.051004 1.905748 16.74099
t-Statistic 1.056660 7.213656 -4.183996 1.874777
Prob. 0.3055 0.0000 0.0006 0.0781
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Durbin-Watson stat
0.889257 Mean dependent var 0.869714 S.D. dependent var 34.31605 Akaike info criterion 20019.05 Schwarz criterion -101.8268 F-statistic
0.966201 Prob(F-statistic)
2250.9286
95.07114 10.07875 10.27770 45.50288 0.000000
由表13可以看出，加入利率R后虽然R=0.869714>0.851512，明显增大，F统计量也比较大。但是利率R的t检验不能通过。则剔除利率R这个变量。因此本模型的回归结果应该是：
CPI=148.9000+0.284208GDP-6.709022X (16.00057) (0.026311) (1.902815)
t=(9.305922)( 10.80198) (-3.525840)
R2=0.866361 R=0.851512 F=58.34546 df=18
下面进行异方差检验：
22、异方差检验：我们的样本属于小样本时间序列，通过ARCH检验，并比较后得到取p=2时，Akaike info
22
criterion取值最小（见表14）。且（n-p）χ=（21-2）*0.382946=7.275974>χ(2)=4.60517，表明模型
中的随机误差项存在异方差。但是鉴于目前的eviews使用能力，不能够保证在一个变量的权数不变时计算另一个变量的权数，因此无法对多变量模型进行异方差的修正。
表14
ARCH Test:
F-statistic 4.964821 Prob. F(2,16) 0.021018
Obs*R-squared 7.275966 Prob. Chi-Square(2) 0.026305
Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/15/07 Time: 13:47 Sample (adjusted): 1987 2005 Included observations: 19 after adjustments
CoefficienVariable t Std. Error t-Statistic Prob.
C 881.5774 458.4473 1.922964 0.0725 RESID^2(-1) 0.796307 0.253800 3.137540 0.0064 RESID^2(-2) -0.510741 0.255340 -2.000241 0.0627
R-squared 0.382946 Mean dependent var 1160.218