Time series data

## [1] "monetary_base-マネタリーベース平均残高(月次):マネタリーベース平均残高:兆円"
##           Jan      Feb      Mar      Apr      May      Jun      Jul      Aug      Sep      Oct      Nov      Dec
## 2013 131.9205 129.3148 134.7413 149.5975 154.1412 163.5375 170.3890 172.4437 181.7012 186.8687 189.7244 193.4594
## 2014 200.4141 201.3223 208.5929 222.0795 224.3719 233.2465 243.1068 242.3138 245.8169 255.7542 259.3603 267.4016
## 2015 275.3859 275.2617 282.1182 300.3275 304.3476 313.0770 322.8211 322.9269 332.1941 338.8877 343.7218 346.3793
## 2016 355.1030 355.0415 362.6050 380.8364 381.8397 392.7119 402.4578 400.9981 407.5081 413.8966 417.6573 426.3922
## 2017 435.2054 430.9696 436.2634 456.2398 455.9954 459.4854 465.0692 466.3075 471.1205 473.8791 472.5834         
## 
## [1] "money_stock-マネーストック(月次):M2/平/マネーストック:兆円"
##           Jan      Feb      Mar      Apr      May      Jun      Jul      Aug      Sep      Oct      Nov      Dec
## 2013 829.9554 828.2805 833.8735 843.7335 844.0305 849.6379 850.5401 849.8909 850.7913 852.0882 855.0157 862.7674
## 2014 865.8882 861.1077 863.4439 872.8308 871.6091 875.3539 875.7077 875.1629 876.8085 878.8933 885.4999 893.2570
## 2015 894.7822 890.9799 894.4203 904.1891 907.1187 909.1087 910.3285 911.2935 909.7766 910.6467 914.6533 920.7139
## 2016 922.7106 918.3897 921.4875 933.7771 936.8614 939.4850 940.5358 940.0505 940.8068 943.0176 949.5360 956.4327
## 2017 959.1393 956.2105 959.8140 970.3462 972.4369 976.4445 978.2352 977.7124 978.8447 981.3254 987.7838
tail(data_set)
cat('\n')
tail(data_set_1stdiff)
##          Date monetary_base money_stock
## 54 2017-06-01      459.4854    976.4445
## 55 2017-07-01      465.0692    978.2352
## 56 2017-08-01      466.3075    977.7124
## 57 2017-09-01      471.1205    978.8447
## 58 2017-10-01      473.8791    981.3254
## 59 2017-11-01      472.5834    987.7838
## 
##          Date monetary_base money_stock
## 53 2017-06-01          3.49        4.01
## 54 2017-07-01          5.58        1.79
## 55 2017-08-01          1.24       -0.52
## 56 2017-09-01          4.81        1.13
## 57 2017-10-01          2.76        2.48
## 58 2017-11-01         -1.30        6.46

Unit root test

Level

fun_adftest <- function(obj,type = c('trend','drift','none'),criterion = 'AIC',max.lag.y = 5){
  library(CADFtest);library(tseries);library(urca)
  print(apply(obj,2,adf.test))
  cat('----------*----------*----------*----------*----------*----------*----------*----------*----------*\n')
  print(lapply(type,function(t){apply(obj,2,function(x){CADFtest(model = x~1, criterion = criterion,type = t,max.lag.y = max.lag.y,dname = paste0('type:',t))})}))
  cat('----------*----------*----------*----------*----------*----------*----------*----------*----------*\n')
  print(apply(obj,2,pp.test))
  cat('----------*----------*----------*----------*----------*----------*----------*----------*----------*\n')
  print(apply(obj,2,function(x)summary(ur.kpss(x))))
}
fun_adftest(obj = data_set[,-1])
## $monetary_base
## 
##  Augmented Dickey-Fuller Test
## 
## data:  newX[, i]
## Dickey-Fuller = -1.897, Lag order = 3, p-value = 0.6163
## alternative hypothesis: stationary
## 
## 
## $money_stock
## 
##  Augmented Dickey-Fuller Test
## 
## data:  newX[, i]
## Dickey-Fuller = -2.6765, Lag order = 3, p-value = 0.3014
## alternative hypothesis: stationary
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## [[1]]
## [[1]]$monetary_base
## 
##  ADF test
## 
## data:  type:trend
## ADF(3) = -1.8954, p-value = 0.6429
## alternative hypothesis: true delta is less than 0
## sample estimates:
##      delta 
## -0.3046792 
## 
## 
## [[1]]$money_stock
## 
##  ADF test
## 
## data:  type:trend
## ADF(2) = -3.1497, p-value = 0.1058
## alternative hypothesis: true delta is less than 0
## sample estimates:
##      delta 
## -0.4093883 
## 
## 
## 
## [[2]]
## [[2]]$monetary_base
## 
##  ADF test
## 
## data:  type:drift
## ADF(4) = -0.92767, p-value = 0.7718
## alternative hypothesis: true delta is less than 0
## sample estimates:
##        delta 
## -0.005504009 
## 
## 
## [[2]]$money_stock
## 
##  ADF test
## 
## data:  type:drift
## ADF(4) = 1.3347, p-value = 0.9985
## alternative hypothesis: true delta is less than 0
## sample estimates:
##      delta 
## 0.01352723 
## 
## 
## 
## [[3]]
## [[3]]$monetary_base
## 
##  ADF test
## 
## data:  type:none
## ADF(3) = 1.7777, p-value = 0.9806
## alternative hypothesis: true delta is less than 0
## sample estimates:
##       delta 
## 0.007782176 
## 
## 
## [[3]]$money_stock
## 
##  ADF test
## 
## data:  type:none
## ADF(4) = 6.0606, p-value = 1
## alternative hypothesis: true delta is less than 0
## sample estimates:
##       delta 
## 0.006005033 
## 
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## $monetary_base
## 
##  Phillips-Perron Unit Root Test
## 
## data:  newX[, i]
## Dickey-Fuller Z(alpha) = -23.081, Truncation lag parameter = 3, p-value = 0.02283
## alternative hypothesis: stationary
## 
## 
## $money_stock
## 
##  Phillips-Perron Unit Root Test
## 
## data:  newX[, i]
## Dickey-Fuller Z(alpha) = -22.591, Truncation lag parameter = 3, p-value = 0.02501
## alternative hypothesis: stationary
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## $monetary_base
## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 3 lags. 
## 
## Value of test-statistic is: 1.5745 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739
## 
## 
## $money_stock
## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 3 lags. 
## 
## Value of test-statistic is: 1.5701 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739

1st difference

fun_adftest(obj = data_set_1stdiff[,-1])
## $monetary_base
## 
##  Augmented Dickey-Fuller Test
## 
## data:  newX[, i]
## Dickey-Fuller = -4.3341, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationary
## 
## 
## $money_stock
## 
##  Augmented Dickey-Fuller Test
## 
## data:  newX[, i]
## Dickey-Fuller = -6.4157, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationary
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## [[1]]
## [[1]]$monetary_base
## 
##  ADF test
## 
## data:  type:trend
## ADF(3) = -4.0793, p-value = 0.0119
## alternative hypothesis: true delta is less than 0
## sample estimates:
##     delta 
## -1.494387 
## 
## 
## [[1]]$money_stock
## 
##  ADF test
## 
## data:  type:trend
## ADF(3) = -6.4172, p-value = 0.00000924
## alternative hypothesis: true delta is less than 0
## sample estimates:
##     delta 
## -2.053757 
## 
## 
## 
## [[2]]
## [[2]]$monetary_base
## 
##  ADF test
## 
## data:  type:drift
## ADF(3) = -3.9842, p-value = 0.003052
## alternative hypothesis: true delta is less than 0
## sample estimates:
##     delta 
## -1.447421 
## 
## 
## [[2]]$money_stock
## 
##  ADF test
## 
## data:  type:drift
## ADF(3) = -6.225, p-value = 0.000002129
## alternative hypothesis: true delta is less than 0
## sample estimates:
##     delta 
## -1.973935 
## 
## 
## 
## [[3]]
## [[3]]$monetary_base
## 
##  ADF test
## 
## data:  type:none
## ADF(5) = -0.9975, p-value = 0.2818
## alternative hypothesis: true delta is less than 0
## sample estimates:
##       delta 
## -0.09801217 
## 
## 
## [[3]]$money_stock
## 
##  ADF test
## 
## data:  type:none
## ADF(5) = -1.1738, p-value = 0.2166
## alternative hypothesis: true delta is less than 0
## sample estimates:
##      delta 
## -0.2082729 
## 
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## $monetary_base
## 
##  Phillips-Perron Unit Root Test
## 
## data:  newX[, i]
## Dickey-Fuller Z(alpha) = -63.773, Truncation lag parameter = 3, p-value = 0.01
## alternative hypothesis: stationary
## 
## 
## $money_stock
## 
##  Phillips-Perron Unit Root Test
## 
## data:  newX[, i]
## Dickey-Fuller Z(alpha) = -40.995, Truncation lag parameter = 3, p-value = 0.01
## alternative hypothesis: stationary
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## $monetary_base
## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 3 lags. 
## 
## Value of test-statistic is: 0.1464 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739
## 
## 
## $money_stock
## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 3 lags. 
## 
## Value of test-statistic is: 0.0586 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739

ACF and CCF

Level

acf(data_set[,-1],lag.max = 12*5)


1st difference

acf(data_set_1stdiff[,-1],lag.max = 12*5)

Run test

1st difference

apply(data_set_1stdiff[,-1],2,function(x) runs.test(factor(sign(x))))
## $monetary_base
## 
##  Runs Test
## 
## data:  factor(sign(x))
## Standard Normal = 0.11759, p-value = 0.9064
## alternative hypothesis: two.sided
## 
## 
## $money_stock
## 
##  Runs Test
## 
## data:  factor(sign(x))
## Standard Normal = 1.3828, p-value = 0.1667
## alternative hypothesis: two.sided

BDS test

Level

apply(data_set[,-1],2,bds.test)
## $monetary_base
## 
##   BDS Test 
## 
## data:  newX[, i] 
## 
## Embedding dimension =  2 3 
## 
## Epsilon for close points =   53.8486 107.6971 161.5457 215.3942 
## 
## Standard Normal = 
##       [ 53.8486 ] [ 107.6971 ] [ 161.5457 ] [ 215.3942 ]
## [ 2 ]    402.5063     191.4224      47.2704      31.3453
## [ 3 ]    841.7457     257.1573      51.9509      31.1702
## 
## p-value = 
##       [ 53.8486 ] [ 107.6971 ] [ 161.5457 ] [ 215.3942 ]
## [ 2 ]           0            0            0            0
## [ 3 ]           0            0            0            0
## 
## 
## 
## $money_stock
## 
##   BDS Test 
## 
## data:  newX[, i] 
## 
## Embedding dimension =  2 3 
## 
## Epsilon for close points =  22.8197 45.6393 68.4590 91.2786 
## 
## Standard Normal = 
##       [ 22.8197 ] [ 45.6393 ] [ 68.459 ] [ 91.2786 ]
## [ 2 ]    1195.830    103.1795    38.3697     28.7113
## [ 3 ]    2398.773    134.3284    41.2561     28.0564
## 
## p-value = 
##       [ 22.8197 ] [ 45.6393 ] [ 68.459 ] [ 91.2786 ]
## [ 2 ]           0           0          0           0
## [ 3 ]           0           0          0           0

1st difference

apply(data_set_1stdiff[,-1],2,bds.test)
## $monetary_base
## 
##   BDS Test 
## 
## data:  newX[, i] 
## 
## Embedding dimension =  2 3 
## 
## Epsilon for close points =   2.5235  5.0469  7.5704 10.0938 
## 
## Standard Normal = 
##       [ 2.5235 ] [ 5.0469 ] [ 7.5704 ] [ 10.0938 ]
## [ 2 ]     2.1437     0.1169     0.5126      0.3334
## [ 3 ]     2.8259     1.6344     1.2671      0.4255
## 
## p-value = 
##       [ 2.5235 ] [ 5.0469 ] [ 7.5704 ] [ 10.0938 ]
## [ 2 ]     0.0321     0.9070     0.6082      0.7388
## [ 3 ]     0.0047     0.1022     0.2051      0.6705
## 
## 
## 
## $money_stock
## 
##   BDS Test 
## 
## data:  newX[, i] 
## 
## Embedding dimension =  2 3 
## 
## Epsilon for close points =  1.8294 3.6587 5.4881 7.3175 
## 
## Standard Normal = 
##       [ 1.8294 ] [ 3.6587 ] [ 5.4881 ] [ 7.3175 ]
## [ 2 ]     0.1021    -1.4342    -1.8408    -2.2032
## [ 3 ]     5.0991     1.1927    -0.1650    -1.1694
## 
## p-value = 
##       [ 1.8294 ] [ 3.6587 ] [ 5.4881 ] [ 7.3175 ]
## [ 2 ]     0.9187     0.1515     0.0656     0.0276
## [ 3 ]     0.0000     0.2330     0.8689     0.2422

Cointegration test

Phillips-Ouliaris Cointegration Test.Null hypothesis:not cointegrated.

po.test(x = data_set[,-1],demean = T,lshort = T)
cat('----------*----------*----------*----------*----------*----------*----------*----------*----------*\n')
summary(ca.jo(x = data_set[,-1]))
## 
##  Phillips-Ouliaris Cointegration Test
## 
## data:  data_set[, -1]
## Phillips-Ouliaris demeaned = -10.564, Truncation lag parameter = 0, p-value = 0.15
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## 
## ###################### 
## # Johansen-Procedure # 
## ###################### 
## 
## Test type: maximal eigenvalue statistic (lambda max) , with linear trend 
## 
## Eigenvalues (lambda):
## [1] 0.14660180 0.04169458
## 
## Values of teststatistic and critical values of test:
## 
##          test 10pct  5pct  1pct
## r <= 1 | 2.43  6.50  8.18 11.65
## r = 0  | 9.04 12.91 14.90 19.19
## 
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
## 
##                  monetary_base.l2 money_stock.l2
## monetary_base.l2         1.000000      1.0000000
## money_stock.l2          -2.404066     -0.8319339
## 
## Weights W:
## (This is the loading matrix)
## 
##                 monetary_base.l2 money_stock.l2
## monetary_base.d        0.1113950  -0.0119571406
## money_stock.d          0.1530457  -0.0005746793

Augmented Dickey-Fuller Test

residual_data <- cbind(resid(lm(money_stock ~ monetary_base, data = data_set)))
fun_adftest(obj = residual_data)
## [[1]]
## 
##  Augmented Dickey-Fuller Test
## 
## data:  newX[, i]
## Dickey-Fuller = -0.46523, Lag order = 3, p-value = 0.9803
## alternative hypothesis: stationary
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## [[1]]
## [[1]][[1]]
## 
##  ADF test
## 
## data:  type:trend
## ADF(2) = -0.98856, p-value = 0.9368
## alternative hypothesis: true delta is less than 0
## sample estimates:
##      delta 
## -0.1028148 
## 
## 
## 
## [[2]]
## [[2]][[1]]
## 
##  ADF test
## 
## data:  type:drift
## ADF(2) = -1.2292, p-value = 0.6552
## alternative hypothesis: true delta is less than 0
## sample estimates:
##      delta 
## -0.1296256 
## 
## 
## 
## [[3]]
## [[3]][[1]]
## 
##  ADF test
## 
## data:  type:none
## ADF(2) = -1.2743, p-value = 0.1842
## alternative hypothesis: true delta is less than 0
## sample estimates:
##     delta 
## -0.132304 
## 
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## [[1]]
## 
##  Phillips-Perron Unit Root Test
## 
## data:  newX[, i]
## Dickey-Fuller Z(alpha) = -8.6889, Truncation lag parameter = 3, p-value = 0.5985
## alternative hypothesis: stationary
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## [[1]]
## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 3 lags. 
## 
## Value of test-statistic is: 0.2236 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739

VAR

Level

library(vars)
fun_var <- function(obj,type=c('const','trend','both','none')){
  print(lapply(type,function(type)VARselect(y = obj,lag.max = 5,type = type)))
  cat('----------*----------*----------*----------*----------*----------*----------*----------*----------*\n')
  var_result <- VAR(y = data_set[,-1],p = 5,type = 'const')
  print(var_result)
  return(var_result)
}
var_result_level <- fun_var(obj = data_set[,-1])
## [[1]]
## [[1]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      5      4      1      5 
## 
## [[1]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.384041   5.323039   5.096611   4.948251   4.923817
## HQ(n)    5.469271   5.465090   5.295482   5.203942   5.236328
## SC(n)    5.605039   5.691370   5.612274   5.611246   5.734144
## FPE(n) 217.950876 205.224216 163.947307 141.815750 139.125539
## 
## 
## [[2]]
## [[2]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      4      4      1      4 
## 
## [[2]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.313658   5.391862   5.039724   4.893042   4.946298
## HQ(n)    5.398889   5.533913   5.238595   5.148733   5.258809
## SC(n)    5.534657   5.760193   5.555387   5.556037   5.756625
## FPE(n) 203.138402 219.845766 154.881218 134.198526 142.288579
## 
## 
## [[3]]
## [[3]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      4      4      1      4 
## 
## [[3]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.197140   5.113230   4.965811   4.795033   4.878693
## HQ(n)    5.310780   5.283691   5.193092   5.079134   5.219615
## SC(n)    5.491804   5.555226   5.555139   5.531693   5.762686
## FPE(n) 180.852787 166.512855 144.056296 121.958248 133.456385
## 
## 
## [[4]]
## [[4]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      5      4      4      5 
## 
## [[4]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.376418   5.401749   5.061741   4.910242   4.900322
## HQ(n)    5.433238   5.515389   5.232202   5.137523   5.184424
## SC(n)    5.523750   5.696413   5.503738   5.499571   5.636983
## FPE(n) 216.260922 221.914559 158.156355 136.269678 135.499595
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## 
## VAR Estimation Results:
## ======================= 
## 
## Estimated coefficients for equation monetary_base: 
## ================================================== 
## Call:
## monetary_base = monetary_base.l1 + money_stock.l1 + monetary_base.l2 + money_stock.l2 + monetary_base.l3 + money_stock.l3 + monetary_base.l4 + money_stock.l4 + monetary_base.l5 + money_stock.l5 + const 
## 
## monetary_base.l1   money_stock.l1 monetary_base.l2   money_stock.l2 monetary_base.l3   money_stock.l3 monetary_base.l4   money_stock.l4 monetary_base.l5   money_stock.l5            const 
##       0.80517349       0.15237054       0.05462996      -0.54714413       0.48362094       0.21925238      -0.57389179       0.09082346       0.33428008      -0.18182275     217.73977012 
## 
## 
## Estimated coefficients for equation money_stock: 
## ================================================ 
## Call:
## money_stock = monetary_base.l1 + money_stock.l1 + monetary_base.l2 + money_stock.l2 + monetary_base.l3 + money_stock.l3 + monetary_base.l4 + money_stock.l4 + monetary_base.l5 + money_stock.l5 + const 
## 
## monetary_base.l1   money_stock.l1 monetary_base.l2   money_stock.l2 monetary_base.l3   money_stock.l3 monetary_base.l4   money_stock.l4 monetary_base.l5   money_stock.l5            const 
##      -0.10181148       1.14060854       0.15380546      -0.74416338      -0.08271678       0.36853272      -0.23442749       0.18393199       0.33918248      -0.12292765     141.53731308

1st difference

var_result_1st_difference <- fun_var(obj = data_set_1stdiff[,-1])
## [[1]]
## [[1]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      5      3      3      5 
## 
## [[1]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.398757   4.988569   4.816732   4.857266   4.762062
## HQ(n)    5.484532   5.131527   5.016874   5.114591   5.076570
## SC(n)    5.621809   5.360322   5.337187   5.526422   5.579919
## FPE(n) 221.184941 146.891515 123.944849 129.529727 118.427389
## 
## 
## [[2]]
## [[2]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      3      3      3      3 
## 
## [[2]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.749125   5.457487   4.894178   5.005236   4.951895
## HQ(n)    5.834900   5.600446   5.094320   5.262561   5.266404
## SC(n)    5.972177   5.829240   5.414633   5.674391   5.769752
## FPE(n) 313.991998 234.771506 133.925390 150.186809 143.184421
## 
## 
## [[3]]
## [[3]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      5      3      3      5 
## 
## [[3]]$criteria
##                 1          2          3          4          5
## AIC(n)   5.420214   4.965544   4.812300   4.854003   4.703084
## HQ(n)    5.534581   5.137094   5.041034   5.139920   5.046184
## SC(n)    5.717617   5.411648   5.407105   5.597510   5.595292
## FPE(n) 226.057554 143.666382 123.587494 129.431964 112.062232
## 
## 
## [[4]]
## [[4]]$selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      3      3      3      3 
## 
## [[4]]$criteria
##                 1          2          3          4          5
## AIC(n)   6.002633   5.676673   5.000091   5.143744   5.181633
## HQ(n)    6.059817   5.791040   5.171641   5.372477   5.467550
## SC(n)    6.151334   5.974075   5.446195   5.738549   5.925139
## FPE(n) 404.521498 292.144359 148.716274 172.154635 179.609535
## 
## 
## ----------*----------*----------*----------*----------*----------*----------*----------*----------*
## 
## VAR Estimation Results:
## ======================= 
## 
## Estimated coefficients for equation monetary_base: 
## ================================================== 
## Call:
## monetary_base = monetary_base.l1 + money_stock.l1 + monetary_base.l2 + money_stock.l2 + monetary_base.l3 + money_stock.l3 + monetary_base.l4 + money_stock.l4 + monetary_base.l5 + money_stock.l5 + const 
## 
## monetary_base.l1   money_stock.l1 monetary_base.l2   money_stock.l2 monetary_base.l3   money_stock.l3 monetary_base.l4   money_stock.l4 monetary_base.l5   money_stock.l5            const 
##       0.80517349       0.15237054       0.05462996      -0.54714413       0.48362094       0.21925238      -0.57389179       0.09082346       0.33428008      -0.18182275     217.73977012 
## 
## 
## Estimated coefficients for equation money_stock: 
## ================================================ 
## Call:
## money_stock = monetary_base.l1 + money_stock.l1 + monetary_base.l2 + money_stock.l2 + monetary_base.l3 + money_stock.l3 + monetary_base.l4 + money_stock.l4 + monetary_base.l5 + money_stock.l5 + const 
## 
## monetary_base.l1   money_stock.l1 monetary_base.l2   money_stock.l2 monetary_base.l3   money_stock.l3 monetary_base.l4   money_stock.l4 monetary_base.l5   money_stock.l5            const 
##      -0.10181148       1.14060854       0.15380546      -0.74416338      -0.08271678       0.36853272      -0.23442749       0.18393199       0.33918248      -0.12292765     141.53731308

Impulse response

Level

plot(irf(x = var_result_level,n.ahead = 12*3,ci = 0.95),plot.type = "multiple",lwd = 1)

1st difference

plot(irf(x = var_result_1st_difference,n.ahead = 12*3,ci = 0.95),plot.type = "multiple",lwd = 1)