setwd("C:/Users/marcogeovanni/Desktop/Financial Econ")
library(vars)
## Warning: package 'vars' was built under R version 3.2.5
## Loading required package: MASS
## Warning: package 'MASS' was built under R version 3.2.3
## Loading required package: strucchange
## Warning: package 'strucchange' was built under R version 3.2.3
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: sandwich
## Warning: package 'sandwich' was built under R version 3.2.3
## Loading required package: urca
## Warning: package 'urca' was built under R version 3.2.3
## Loading required package: lmtest
## Warning: package 'lmtest' was built under R version 3.2.3
library(readstata13)
library(ggplot2)
library(tseries)
## Warning: package 'tseries' was built under R version 3.2.4
library(urca)
library(forecast)
## Warning: package 'forecast' was built under R version 3.2.3
## Loading required package: timeDate
## Warning: package 'timeDate' was built under R version 3.2.3
## This is forecast 6.2
CSeries<- read.dta13("currencies.dta")
attach(CSeries)
summary(CSeries)
## Date EUR GBP JPY
## Min. :2002-07-07 Min. :0.6269 Min. :0.4751 Min. : 75.84
## 1st Qu.:2005-03-29 1st Qu.:0.7305 1st Qu.:0.5386 1st Qu.: 89.39
## Median :2007-12-21 Median :0.7701 Median :0.6071 Median :105.77
## Mean :2007-12-21 Mean :0.7783 Mean :0.5891 Mean :101.93
## 3rd Qu.:2010-09-13 3rd Qu.:0.8151 3rd Qu.:0.6339 3rd Qu.:115.85
## Max. :2013-06-06 Max. :1.0353 Max. :0.7283 Max. :125.56
##
## reur rgbp rjpy
## Min. :-3.459632 Min. :-3.138631 Min. :-3.663029
## 1st Qu.:-0.230957 1st Qu.:-0.201699 1st Qu.:-0.221085
## Median : 0.000000 Median : 0.000000 Median : 0.000000
## Mean :-0.007413 Mean :-0.000226 Mean :-0.004699
## 3rd Qu.: 0.196187 3rd Qu.: 0.194153 3rd Qu.: 0.209187
## Max. : 2.524495 Max. : 3.989872 Max. : 2.852516
## NA's :1 NA's :1 NA's :1
## cvar_rjpy_stat cvar_rjpy_dyn
## Min. :0.05304 Min. :0.05608
## 1st Qu.:0.14595 1st Qu.:0.16856
## Median :0.19982 Median :0.23231
## Mean :0.22041 Mean :0.25200
## 3rd Qu.:0.26595 3rd Qu.:0.32401
## Max. :1.93546 Max. :1.93546
##
Reur<- reur[2:3988]
Rgbp<- rgbp[2:3988]
Rjpy<- rjpy[2:3988]
Date2<-Date[2:3988]
RelateVar<-data.frame(Reur,Rgbp,Rjpy)
ExchangerateseriesPlot<-ggplot(data=RelateVar, aes(Rjpy))+ geom_line(aes(Date2, Rjpy), color="blue")
ExchangerateseriesPlot+geom_line(aes(Date2, Rgbp, color="red"))+geom_line(aes(Date2, Reur, color="green"))+ggtitle("Yen,Pound,Euro Against Dollar Exchange Rate")+xlab("year")+ylab("Exchange Rate")+guides(color="none")
adf.test(Reur)
## Warning in adf.test(Reur): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: Reur
## Dickey-Fuller = -15.201, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary
adf.test(Rgbp)
## Warning in adf.test(Rgbp): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: Rgbp
## Dickey-Fuller = -16.657, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary
adf.test(Rjpy)
## Warning in adf.test(Rjpy): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: Rjpy
## Dickey-Fuller = -15.292, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary
VARselect(RelateVar, lag.max = 20)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 2 2 1 2
##
## $criteria
## 1 2 3 4 5
## AIC(n) -5.469043044 -5.47724777 -5.474945446 -5.474425715 -5.473741426
## HQ(n) -5.462300181 -5.46544776 -5.458088289 -5.452511411 -5.446769975
## SC(n) -5.450028881 -5.44397299 -5.427410038 -5.412629685 -5.397684774
## FPE(n) 0.004215264 0.00418082 0.004190457 0.004192636 0.004195506
## 6 7 8 9 10
## AIC(n) -5.472123084 -5.472306262 -5.471337538 -5.469260168 -5.466648533
## HQ(n) -5.440094485 -5.435220517 -5.429194645 -5.422060129 -5.414391346
## SC(n) -5.381805809 -5.367728365 -5.352499019 -5.336161027 -5.319288768
## FPE(n) 0.004202302 0.004201533 0.004205605 0.004214352 0.004225374
## 11 12 13 14 15
## AIC(n) -5.46554261 -5.467658364 -5.467499358 -5.466952139 -5.464793502
## HQ(n) -5.40822828 -5.405286883 -5.400070730 -5.394466363 -5.387250579
## SC(n) -5.30392223 -5.291777355 -5.277357727 -5.262549885 -5.246130626
## FPE(n) 0.00423005 0.004221112 0.004221785 0.004224098 0.004233228
## 16 17 18 19 20
## AIC(n) -5.466572632 -5.464644685 -5.462538230 -5.460842203 -5.468775916
## HQ(n) -5.383972562 -5.376987468 -5.369823866 -5.363070692 -5.365947258
## SC(n) -5.233649134 -5.217460564 -5.201093487 -5.185136838 -5.178809929
## FPE(n) 0.004225706 0.004233864 0.004242796 0.004250001 0.004216421
MVar2<-VAR(RelateVar, p=2)
summary(MVar2)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Reur, Rgbp, Rjpy
## Deterministic variables: const
## Sample size: 3985
## Log Likelihood: -6043.54
## Roots of the characteristic polynomial:
## 0.3329 0.3329 0.1532 0.1146 0.1146 0.002806
## Call:
## VAR(y = RelateVar, p = 2)
##
##
## Estimation results for equation Reur:
## =====================================
## Reur = Reur.l1 + Rgbp.l1 + Rjpy.l1 + Reur.l2 + Rgbp.l2 + Rjpy.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Reur.l1 0.200155 0.022708 8.814 <2e-16 ***
## Rgbp.l1 -0.061566 0.024107 -2.554 0.0107 *
## Rjpy.l1 -0.020151 0.016658 -1.210 0.2265
## Reur.l2 -0.033413 0.022619 -1.477 0.1397
## Rgbp.l2 0.024656 0.024079 1.024 0.3059
## Rjpy.l2 0.002628 0.016682 0.158 0.8748
## const -0.005836 0.007453 -0.783 0.4337
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.4703 on 3978 degrees of freedom
## Multiple R-Squared: 0.02548, Adjusted R-squared: 0.02401
## F-statistic: 17.33 on 6 and 3978 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation Rgbp:
## =====================================
## Rgbp = Reur.l1 + Rgbp.l1 + Rjpy.l1 + Reur.l2 + Rgbp.l2 + Rjpy.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Reur.l1 -4.278e-02 2.079e-02 -2.058 0.039687 *
## Rgbp.l1 2.616e-01 2.207e-02 11.855 < 2e-16 ***
## Rjpy.l1 -5.664e-02 1.525e-02 -3.714 0.000207 ***
## Reur.l2 5.677e-02 2.071e-02 2.741 0.006144 **
## Rgbp.l2 -9.210e-02 2.204e-02 -4.178 3.01e-05 ***
## Rjpy.l2 2.964e-03 1.527e-02 0.194 0.846115
## const 4.539e-05 6.823e-03 0.007 0.994693
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.4306 on 3978 degrees of freedom
## Multiple R-Squared: 0.05224, Adjusted R-squared: 0.05081
## F-statistic: 36.55 on 6 and 3978 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation Rjpy:
## =====================================
## Rjpy = Reur.l1 + Rgbp.l1 + Rjpy.l1 + Reur.l2 + Rgbp.l2 + Rjpy.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Reur.l1 0.0241862 0.0225072 1.075 0.28262
## Rgbp.l1 -0.0679786 0.0238946 -2.845 0.00446 **
## Rjpy.l1 0.1508446 0.0165107 9.136 < 2e-16 ***
## Reur.l2 -0.0313338 0.0224194 -1.398 0.16231
## Rgbp.l2 0.0324034 0.0238668 1.358 0.17464
## Rjpy.l2 0.0007184 0.0165350 0.043 0.96535
## const -0.0036822 0.0073871 -0.498 0.61818
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.4662 on 3978 degrees of freedom
## Multiple R-Squared: 0.0243, Adjusted R-squared: 0.02283
## F-statistic: 16.51 on 6 and 3978 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## Reur Rgbp Rjpy
## Reur 0.22118 0.1417 0.06108
## Rgbp 0.14168 0.1854 0.03390
## Rjpy 0.06108 0.0339 0.21730
##
## Correlation matrix of residuals:
## Reur Rgbp Rjpy
## Reur 1.0000 0.6997 0.2786
## Rgbp 0.6997 1.0000 0.1689
## Rjpy 0.2786 0.1689 1.0000
causality(MVar2, cause=c("Reur","Rgbp"))#Prueba la Causalidad de Una Variable a otra
## $Granger
##
## Granger causality H0: Reur Rgbp do not Granger-cause Rjpy
##
## data: VAR object MVar2
## F-Test = 2.7215, df1 = 4, df2 = 11934, p-value = 0.02792
##
##
## $Instant
##
## H0: No instantaneous causality between: Reur Rgbp and Rjpy
##
## data: VAR object MVar2
## Chi-squared = 291.62, df = 2, p-value < 2.2e-16
irf(MVar2)
##
## Impulse response coefficients
## $Reur
## Reur Rgbp Rjpy
## [1,] 4.703010e-01 3.012473e-01 1.298798e-01
## [2,] 7.296946e-02 5.134498e-02 1.048809e-02
## [3,] 3.287276e-03 9.058486e-03 -5.025027e-03
## [4,] -9.431050e-04 1.958896e-03 -1.909401e-03
## [5,] -1.705911e-04 -1.528698e-06 -2.570835e-04
## [6,] 4.592291e-05 -2.181542e-04 4.885252e-05
## [7,] 2.662487e-05 -7.211572e-05 2.842071e-05
## [8,] 2.411402e-06 1.226389e-06 1.360616e-06
## [9,] -2.213290e-06 8.378179e-06 -2.970439e-06
## [10,] -9.457137e-07 2.482991e-06 -1.105985e-06
## [11,] -4.715073e-08 -1.533211e-07 -1.979724e-08
##
## $Rgbp
## Reur Rgbp Rjpy
## [1,] 0.000000e+00 3.076315e-01 -1.698554e-02
## [2,] -1.859731e-02 8.145162e-02 -2.347455e-02
## [3,] -7.236329e-04 -4.946453e-03 4.283215e-04
## [4,] 2.719042e-03 -9.914460e-03 3.588530e-03
## [5,] 9.856552e-04 -2.497859e-03 1.143745e-03
## [6,] 2.146562e-06 3.176172e-04 -3.771386e-05
## [7,] -1.098803e-04 3.745426e-04 -1.382300e-04
## [8,] -3.460635e-05 8.128385e-05 -3.877221e-05
## [9,] 1.393276e-06 -1.619891e-05 3.268972e-06
## [10,] 4.268855e-06 -1.404877e-05 5.318351e-06
## [11,] 1.174825e-06 -2.578908e-06 1.294301e-06
##
## $Rjpy
## Reur Rgbp Rjpy
## [1,] 0.000000e+00 0.000000e+00 4.473691e-01
## [2,] -9.014880e-03 -2.533835e-02 6.748322e-02
## [3,] -4.285766e-04 -8.739987e-03 1.200531e-02
## [4,] 6.420457e-05 -9.264998e-04 1.904606e-03
## [5,] -1.381112e-04 4.631647e-04 9.068321e-05
## [6,] -7.796996e-05 2.165757e-04 -5.181183e-05
## [7,] -1.162284e-05 1.270664e-05 -5.023046e-06
## [8,] 4.801522e-06 -2.042003e-05 7.521068e-06
## [9,] 2.755122e-06 -7.819121e-06 3.411086e-06
## [10,] 3.199602e-07 -1.813349e-07 3.059883e-07
## [11,] -2.068422e-07 8.081894e-07 -2.710217e-07
##
##
## Lower Band, CI= 0.95
## $Reur
## Reur Rgbp Rjpy
## [1,] 4.562045e-01 2.831630e-01 1.082056e-01
## [2,] 5.932800e-02 3.561279e-02 -2.787018e-03
## [3,] -9.405366e-03 -3.383382e-03 -1.845758e-02
## [4,] -4.530069e-03 -2.586300e-03 -6.109478e-03
## [5,] -7.928753e-04 -7.853093e-04 -1.009394e-03
## [6,] -1.922830e-04 -6.206980e-04 -1.526621e-04
## [7,] -2.502907e-05 -2.382603e-04 -3.274611e-05
## [8,] -3.286060e-05 -2.275970e-05 -2.325142e-05
## [9,] -2.406029e-05 -3.550216e-06 -2.417324e-05
## [10,] -3.772872e-06 -1.697968e-06 -6.418455e-06
## [11,] -9.695432e-07 -2.058059e-06 -6.114350e-07
##
## $Rgbp
## Reur Rgbp Rjpy
## [1,] 0.000000e+00 2.940488e-01 -4.009858e-02
## [2,] -3.277964e-02 6.746952e-02 -3.893909e-02
## [3,] -1.503480e-02 -1.825436e-02 -1.046814e-02
## [4,] -5.239122e-03 -1.718801e-02 -7.073060e-04
## [5,] -8.486345e-05 -4.166805e-03 7.378405e-05
## [6,] -9.535516e-04 -2.910709e-04 -7.684882e-04
## [7,] -4.790366e-04 4.342114e-05 -4.889801e-04
## [8,] -8.061430e-05 1.783231e-05 -1.017326e-04
## [9,] -2.101843e-05 -8.162549e-05 -1.027753e-05
## [10,] -6.852503e-06 -4.310265e-05 -3.245952e-07
## [11,] -3.075061e-06 -7.651137e-06 -8.177993e-07
##
## $Rjpy
## Reur Rgbp Rjpy
## [1,] 0.000000e+00 0.000000e+00 4.297476e-01
## [2,] -2.117819e-02 -3.664643e-02 5.178169e-02
## [3,] -1.754718e-02 -2.105907e-02 -2.650812e-03
## [4,] -5.752681e-03 -5.958066e-03 -2.981759e-03
## [5,] -1.476949e-03 -7.724453e-04 -8.465215e-04
## [6,] -4.190289e-04 -3.130210e-04 -2.792599e-04
## [7,] -1.049181e-04 -1.811951e-04 -8.002979e-05
## [8,] -1.918414e-05 -7.374536e-05 -6.397351e-06
## [9,] -7.957330e-06 -2.688000e-05 -5.338913e-06
## [10,] -4.832949e-06 -5.600884e-06 -3.614574e-06
## [11,] -1.881754e-06 -5.711710e-07 -1.486963e-06
##
##
## Upper Band, CI= 0.95
## $Reur
## Reur Rgbp Rjpy
## [1,] 4.877603e-01 3.232676e-01 1.523258e-01
## [2,] 8.573593e-02 6.548451e-02 2.476375e-02
## [3,] 1.620040e-02 2.365610e-02 7.175362e-03
## [4,] 3.169800e-03 7.402480e-03 2.184518e-03
## [5,] 1.294136e-03 1.406899e-03 5.825249e-04
## [6,] 6.158333e-04 1.728314e-04 4.725946e-04
## [7,] 1.533136e-04 6.447985e-05 1.367993e-04
## [8,] 2.921900e-05 3.877241e-05 1.278522e-05
## [9,] 8.329595e-06 3.063713e-05 2.683671e-06
## [10,] 2.292569e-06 1.161401e-05 7.228303e-07
## [11,] 2.227868e-06 1.047342e-06 1.222109e-06
##
## $Rgbp
## Reur Rgbp Rjpy
## [1,] 0.000000e+00 3.200753e-01 4.537329e-03
## [2,] -4.189750e-03 9.545688e-02 -8.274688e-03
## [3,] 1.522630e-02 9.312853e-03 1.345651e-02
## [4,] 1.116170e-02 -3.053628e-03 1.053180e-02
## [5,] 2.222506e-03 -1.098934e-03 2.568594e-03
## [6,] 5.508034e-04 1.210211e-03 3.212432e-04
## [7,] 1.923781e-04 9.019968e-04 1.491288e-05
## [8,] 2.210776e-05 1.757228e-04 -1.592284e-06
## [9,] 5.784316e-05 1.511687e-05 3.833925e-05
## [10,] 1.833552e-05 -1.043189e-07 2.212304e-05
## [11,] 3.392327e-06 2.306371e-06 4.448112e-06
##
## $Rjpy
## Reur Rgbp Rjpy
## [1,] 0.000000e+00 0.000000e+00 4.648242e-01
## [2,] 8.846286e-03 -9.450392e-03 8.209440e-02
## [3,] 1.210928e-02 5.599959e-03 2.351000e-02
## [4,] 3.617798e-03 5.040655e-03 5.485474e-03
## [5,] 6.576941e-04 1.432340e-03 1.539293e-03
## [6,] 1.445269e-04 6.702490e-04 3.741675e-04
## [7,] 7.936940e-05 1.300851e-04 1.113203e-04
## [8,] 3.474460e-05 9.103575e-06 3.741323e-05
## [9,] 1.688888e-05 5.365883e-06 1.470749e-05
## [10,] 3.401771e-06 6.040077e-06 5.661356e-06
## [11,] 6.661146e-07 4.184249e-06 7.133929e-07
fevd(MVar2)
## $Reur
## Reur Rgbp Rjpy
## [1,] 1.0000000 0.000000000 0.0000000000
## [2,] 0.9981178 0.001524051 0.0003581120
## [3,] 0.9981148 0.001526281 0.0003589032
## [4,] 0.9980823 0.001558801 0.0003589082
## [5,] 0.9980779 0.001563074 0.0003589907
## [6,] 0.9980779 0.001563074 0.0003590174
## [7,] 0.9980779 0.001563127 0.0003590180
## [8,] 0.9980778 0.001563133 0.0003590181
## [9,] 0.9980778 0.001563133 0.0003590181
## [10,] 0.9980778 0.001563133 0.0003590181
##
## $Rgbp
## Reur Rgbp Rjpy
## [1,] 0.4895160 0.5104840 0.000000000
## [2,] 0.4781687 0.5185439 0.003287417
## [3,] 0.4781410 0.5181839 0.003675103
## [4,] 0.4779089 0.5184136 0.003677557
## [5,] 0.4778931 0.5184284 0.003678533
## [6,] 0.4778929 0.5184284 0.003678769
## [7,] 0.4778925 0.5184287 0.003678767
## [8,] 0.4778925 0.5184287 0.003678769
## [9,] 0.4778925 0.5184287 0.003678769
## [10,] 0.4778925 0.5184287 0.003678769
##
## $Rjpy
## Reur Rgbp Rjpy
## [1,] 0.07763026 0.001327719 0.9210420
## [2,] 0.07630518 0.003773124 0.9199217
## [3,] 0.07636047 0.003771074 0.9198685
## [4,] 0.07636993 0.003828557 0.9198015
## [5,] 0.07636975 0.003834408 0.9197958
## [6,] 0.07636976 0.003834414 0.9197958
## [7,] 0.07636976 0.003834499 0.9197957
## [8,] 0.07636976 0.003834506 0.9197957
## [9,] 0.07636976 0.003834506 0.9197957
## [10,] 0.07636976 0.003834506 0.9197957
plot(fevd(MVar2))
plot(irf(MVar2))
predict(MVar2)
## $Reur
## fcst lower upper CI
## [1,] 0.003939146 -0.9178340 0.9257123 0.9217731
## [2,] -0.006589958 -0.9402711 0.9270912 0.9336811
## [3,] -0.008714573 -0.9424194 0.9249903 0.9337048
## [4,] -0.007438160 -0.9411600 0.9262837 0.9337219
## [5,] -0.006858739 -0.9405827 0.9268652 0.9337240
## [6,] -0.006842066 -0.9405661 0.9268819 0.9337240
## [7,] -0.006904289 -0.9406283 0.9268197 0.9337240
## [8,] -0.006925787 -0.9406498 0.9267982 0.9337240
## [9,] -0.006925600 -0.9406496 0.9267984 0.9337240
## [10,] -0.006923160 -0.9406472 0.9268009 0.9337240
##
## $Rgbp
## fcst lower upper CI
## [1,] -3.887316e-02 -0.8827670 0.8050207 0.8438939
## [2,] 1.018516e-02 -0.8559766 0.8763469 0.8661617
## [3,] 7.379204e-03 -0.8591880 0.8739464 0.8665672
## [4,] 1.439979e-03 -0.8653555 0.8682355 0.8667955
## [5,] -1.717905e-04 -0.8669816 0.8666380 0.8668098
## [6,] -3.736171e-05 -0.8668476 0.8667728 0.8668102
## [7,] 1.799013e-04 -0.8666306 0.8669904 0.8668105
## [8,] 2.323263e-04 -0.8665782 0.8670429 0.8668105
## [9,] 2.245481e-04 -0.8665860 0.8670351 0.8668106
## [10,] 2.163148e-04 -0.8665942 0.8670269 0.8668106
##
## $Rjpy
## fcst lower upper CI
## [1,] -0.032035290 -0.9456737 0.8816031 0.9136384
## [2,] -0.011974384 -0.9365113 0.9125625 0.9245369
## [3,] -0.007746346 -0.9326355 0.9171428 0.9248891
## [4,] -0.005035225 -0.9299662 0.9198958 0.9249310
## [5,] -0.004212968 -0.9291468 0.9207209 0.9249338
## [6,] -0.004195853 -0.9291297 0.9207380 0.9249339
## [7,] -0.004271798 -0.9292057 0.9206621 0.9249339
## [8,] -0.004295682 -0.9292296 0.9206382 0.9249339
## [9,] -0.004294433 -0.9292283 0.9206395 0.9249339
## [10,] -0.004291357 -0.9292253 0.9206426 0.9249339
accuracy(MVar2$varresult[[1]])
## ME RMSE MAE MPE MAPE MASE
## Training set 1.560664e-17 0.4698878 0.3252718 NaN Inf 1.002421