># 单方程误差修正模型案例分析
> ###########################
> # 数据的生成 > set.seed(12345) > u<-rnorm(500) > x<-cumsum(u)#求累积和，返回一个变量，它的第i个元素是从U（1）到U（i）和。 > y<-x+u > # E-G协整估计及检验 > model.lm<-lm(y~x) > summary(model.lm) 对cumsum()函数举例
> x=c(1,3,2,5)
> cumsum(x)
[1] 1 4 6 11
Call: lm(formula = y ~ x)Residuals:Min 1Q Median 3Q Max -2.65130 -0.65274 0.02012 0.60176 2.66642 Coefficients:Estimate Std. Error t value Pr(>|t|) (Intercept) 0.12350 0.10797 1.144 0.253 x 0.99861 0.00333 299.924 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.991 on 498 degrees of freedom Multiple R-squared: 0.9945, Adjusted R-squared: 0.9945 F-statistic: 8.995e+04 on 1 and 498 DF, p-value: < 2.2e-16第一步建立协整关系，利用OLS法得到X和Y的协整回归方程：
> #提取协整回归残差 > re.lm<-resid(model.lm) > #协整检验，应用包urca > summary(ur.df(re.lm,type="none",selectlags="AIC"))#单位根检验，type="trend"有趋势项 ############################################### # Augmented Dickey-Fuller Test Unit Root Test # ############################################### Test regression none Call: lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)Residuals:Min 1Q Median 3Q Max -2.70068 -0.66375 0.03806 0.61796 2.65938 Coefficients:Estimate Std. Error t value Pr(>|t|) z.lag.1 -1.04076 0.06345 -16.404 <2e-16 *** z.diff.lag 0.03986 0.04485 0.889 0.375 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.9916 on 496 degrees of freedom Multiple R-squared: 0.5013, Adjusted R-squared: 0.4993 F-statistic: 249.3 on 2 and 496 DF, p-value: < 2.2e-16Value of test-statistic is: -16.4041 Critical values for test statistics: 1pct 5pct 10pct tau1 -2.58 -1.95 -1.62 > dy<-diff(y) > dx<-diff(x) > error.term<-head(re.lm,-1) > data.ecm<-data.frame(dy=dy,dx=dx,error.term=error.term) > model.ecm<-lm(dy~dx+error.term,data=data.ecm) > summary(model.ecm) Call: lm(formula = dy ~ dx + error.term, data = data.ecm)Residuals:Min 1Q Median 3Q Max -0.043268 -0.008857 -0.001662 0.016696 0.035626 Coefficients:Estimate Std. Error t value Pr(>|t|) (Intercept) -0.0823551 0.0008290 -99.34 <2e-16 *** dx 1.9983047 0.0008346 2394.21 <2e-16 *** error.term -0.9999880 0.0008347 -1198.03 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.01846 on 496 degrees of freedom Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999 F-statistic: 3.585e+06 on 2 and 496 DF, p-value: < 2.2e-16
第二步建立误差修正模型，估计结果为：
其中，误差校正项为
误差校正系数为0.9999880.
