单方程误差修正模型案例分析

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) y<-x+u

E-G协整估计及检验

model.lm<-lm(y~x) summary(model.lm) 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 ‘ ’ 1 Residual 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")) ############################################### # 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 ‘ ’ 1 Residual 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-16 Value 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 ‘ ’ 1 Residual 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.