1 数据
仍然采用2016年至2020年的shibor数据构建VAR模型，分析我们长期利率和短期利率之间的相互影响。
2 加载数据
打开Excel中的数据，复制前两列，如下图所示。
> shibor2=read.table("clipboard",header = TRUE)
> library(xts)
> sb2=as.xts(shibor2)
> sb2
dir wir
2016-01-04 1.9950 2.3350
2016-01-05 1.9980 2.3300
2016-01-06 1.9800 2.3220
2016-01-07 1.9660 2.3130
2016-01-08 1.9580 2.3080
2016-01-11 1.9510 2.3030
2016-01-12 1.9510 2.3000
2016-01-13 1.9500 2.3000
2016-01-14 1.9500 2.3000
2016-01-15 1.9560 2.3030
说明：读取数据并转换成时间序列数据。
3 VAR模型分析
3.1 确定VAR模型的滞后期
> install.packages("vars")
> library(vars)
> library(lmtest)
> VARselect(sb2,lag.max=10,type="const")
$selection
AIC(n) HQ(n) SC(n) FPE(n)
10 6 5 10
说明：采用VARselect()函数自动选择最优滞后阶数！这里采用HQ方法，选择滞后期为6期。
3.2 估计VAR方程
> fit_var=VAR(sb2, p = 6, type = "none")
> summary(fit_var)
VAR Estimation Results:
=========================
Endogenous variables: dir, wir
Deterministic variables: none
Sample size: 1242
Log Likelihood: 2395.856
Roots of the characteristic polynomial:
0.9999 0.8994 0.7271 0.7271 0.6471 0.6471 0.5777 0.5777 0.5289 0.5289 0.2362 0.1451
Call:
VAR(y = sb2, p = 6, type = "none")
Estimation results for equation dir:
====================================
dir = dir.l1 + wir.l1 + dir.l2 + wir.l2 + dir.l3 + wir.l3 + dir.l4 + wir.l4 + dir.l5 + wir.l5 + dir.l6 + wir.l6
Estimate Std. Error t value Pr(>|t|)
dir.l1 1.009195 0.032938 30.639 < 2e-16 ***
wir.l1 0.445452 0.085004 5.240 1.88e-07 ***
dir.l2 -0.223972 0.046408 -4.826 1.57e-06 ***
wir.l2 -0.229660 0.113201 -2.029 0.042696 *
dir.l3 -0.029756 0.046473 -0.640 0.522106
wir.l3 0.059198 0.113246 0.523 0.601250
dir.l4 0.161469 0.046484 3.474 0.000531 ***
wir.l4 -0.395249 0.113128 -3.494 0.000493 ***
dir.l5 0.034306 0.046064 0.745 0.456569
wir.l5 -0.009601 0.114548 -0.084 0.933218
dir.l6 -0.061872 0.032251 -1.918 0.055287 .
wir.l6 0.226027 0.087527 2.582 0.009927 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1604 on 1230 degrees of freedom
Multiple R-Squared: 0.995, Adjusted R-squared: 0.9949
F-statistic: 2.022e+04 on 12 and 1230 DF, p-value: < 2.2e-16
Estimation results for equation wir:
====================================
wir = dir.l1 + wir.l1 + dir.l2 + wir.l2 + dir.l3 + wir.l3 + dir.l4 + wir.l4 + dir.l5 + wir.l5 + dir.l6 + wir.l6
Estimate Std. Error t value Pr(>|t|)
dir.l1 0.01622 0.01270 1.278 0.201601
wir.l1 0.95966 0.03277 29.285 < 2e-16 ***
dir.l2 -0.01420 0.01789 -0.794 0.427355
wir.l2 -0.11941 0.04364 -2.736 0.006306 **
dir.l3 0.01721 0.01792 0.961 0.336889
wir.l3 0.05637 0.04366 1.291 0.196910
dir.l4 -0.02278 0.01792 -1.271 0.203879
wir.l4 -0.06895 0.04361 -1.581 0.114119
dir.l5 0.04542 0.01776 2.558 0.010660 *
wir.l5 0.02402 0.04416 0.544 0.586538
dir.l6 -0.04384 0.01243 -3.526 0.000437 ***
wir.l6 0.14986 0.03374 4.441 9.75e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.06184 on 1230 degrees of freedom
Multiple R-Squared: 0.9994, Adjusted R-squared: 0.9994
F-statistic: 1.746e+05 on 12 and 1230 DF, p-value: < 2.2e-16
说明：特征根均小于1，因而VAR模型平稳！
3.3 脉冲响应分析
> fit_irf=irf(fit_var, impulse =c("dir", "wir"), response = c("dir", "wir"), boot =TRUE)
> fit_irf
Impulse response coefficients
$dir
dir wir
[1,] 0.16041544 0.03093850
[2,] 0.17567210 0.03229313
[3,] 0.14863865 0.02786771
[4,] 0.11271534 0.02730866
[5,] 0.09658360 0.02165304
[6,] 0.09363509 0.02341407
[7,] 0.09235393 0.02456126
[8,] 0.08487094 0.02393352
[9,] 0.07633091 0.02277386
[10,] 0.06954698 0.02231456
[11,] 0.06380204 0.02157746
$wir
dir wir
[1,] 0.000000000 0.05354620
[2,] 0.023852247 0.05138637
[3,] 0.034664310 0.04330690
[4,] 0.040300413 0.03866601
[5,] 0.021353319 0.03171151
[6,] 0.002328567 0.02582680
[7,] 0.003786989 0.03017233
[8,] 0.014188013 0.03374029
[9,] 0.022599291 0.03550523
[10,] 0.026212114 0.03590071
[11,] 0.025168969 0.03483890
说明：$dir表示dir为脉冲，其下方的dir和wir为响应系数；同理，$wir表示dir为脉冲，其下方的dir和wir为响应系数。
> plot(fit_irf$irf$dir[,1],type='l',main="Resonpose of dir to dir",ylab="",xlab=fit_irf$response[1])
> lines(fit_irf$Lower$dir[,1],type="l",lty=2,col="red")
> lines(fit_irf$Upper$dir[,1],type="l",lty=2,col="red")
> plot(fit_irf$irf$dir[,2],type='l',main="Resonpose of wir to dir",ylab="",xlab=fit_irf$response[2])
> lines(fit_irf$Lower$dir[,2],type="l",lty=2,col="red")
> lines(fit_irf$Upper$dir[,2],type="l",lty=2,col="red")
wir为脉冲对应的两个响应图不再演示！
3.4 方差分解分析
> fit_fevd=fevd(fit_var, n.ahead = 100)
> plot(fit_fevd$wir[,1],type='l',col=1,ylab='预测方差贡献率',xlab="",main="Percent dir variance due to wir")
> plot(fit_fevd$wir[,2],type='l',col=1,ylab='预测方差贡献率',xlab="",main="Percent wir variance due to wir")
dir为脉冲对应的两个方差分解图不再演示！