下記は、株価指数の対数値と各世代人口について、、Rを用いて1次の2変量VARモデルにより分析した結果である。80歳以上から分析を始めたところ、55-59世代人口で初めて株価指数にプラスの影響が出た。つまり、60歳以上の人口は、グランジャーの因果性は認められないものの、株価指数にとって負の影響を与えるということである。
> library(vars)
> J<-read.table("c:\\JAPAN.txt",header=T)
> n<-J[,1]
> p80<-J[,18]
> J2<-data.frame(n,p80)
> var2.p<-VAR(J2,p=1,type="const")
> B(var2.p)
n.l1 p80.l1 const
n 0.9439823 -1.471845e-05 0.5797968
p80 1.2049264 1.052066e+00 -8.2186900
警告メッセージ:
Function 'B' is deprecated; use 'Acoef' instead.
See help("vars-deprecated") and help("B-deprecated") for more information.
>
> causality(var2.p,cause="p80")
$Granger
Granger causality H0: p80 do not Granger-cause n
data: VAR object var2.p
F-Test = 0.6104, df1 = 1, df2 = 116, p-value = 0.4362
$Instant
H0: No instantaneous causality between: p80 and n
data: VAR object var2.p
Chi-squared = 0.8211, df = 1, p-value = 0.3649
> impulse<-irf(var2.p,impulse="p80",response=c("n"),boot=FALSE)
> p75<-J[,17]
> J2<-data.frame(n,p75)
> var2.p<-VAR(J2,p=1,type="const")
> B(var2.p)
n.l1 p75.l1 const
n 0.9415225 -1.554662e-05 0.6013296
p75 6.6539352 1.025235e+00 -31.5003987
警告メッセージ:
Function 'B' is deprecated; use 'Acoef' instead.
See help("vars-deprecated") and help("B-deprecated") for more information.
> causality(var2.p,cause="p75")
$Granger
Granger causality H0: p75 do not Granger-cause n
data: VAR object var2.p
F-Test = 0.2931, df1 = 1, df2 = 116, p-value = 0.5893
$Instant
H0: No instantaneous causality between: p75 and n
data: VAR object var2.p
Chi-squared = 1.637, df = 1, p-value = 0.2007
> impulse<-irf(var2.p,impulse="p75",response=c("n"),boot=FALSE)
> plot(impulse)
> p70<-J[,16]
> J2<-data.frame(n,p70)
> var2.p<-VAR(J2,p=1,type="const")
> B(var2.p)
n.l1 p70.l1 const
n 0.9385841 -9.537914e-06 0.6207369
p70 21.6744240 1.005485e+00 -107.9120516
警告メッセージ:
Function 'B' is deprecated; use 'Acoef' instead.
See help("vars-deprecated") and help("B-deprecated") for more information.
> causality(var2.p,cause="p70")
$Granger
Granger causality H0: p70 do not Granger-cause n
data: VAR object var2.p
F-Test = 0.144, df1 = 1, df2 = 116, p-value = 0.705
$Instant
H0: No instantaneous causality between: p70 and n
data: VAR object var2.p
Chi-squared = 0.1523, df = 1, p-value = 0.6963
> impulse<-irf(var2.p,impulse="p70",response=c("n"),boot=FALSE)
> plot(impulse)
>
> impulse<-irf(var2.p,impulse="p70",response=c("n"),boot=FALSE)
> plot(impulse)
> p65<-J[,15]
> J2<-data.frame(n,p65)
> var2.p<-VAR(J2,p=1,type="const")
> B(var2.p)
n.l1 p65.l1 const
n 0.9456698 -1.465275e-05 0.5918841
p65 30.3599273 1.000981e+00 -151.2865065
警告メッセージ:
Function 'B' is deprecated; use 'Acoef' instead.
See help("vars-deprecated") and help("B-deprecated") for more information.
> causality(var2.p,cause="p65")
$Granger
Granger causality H0: p65 do not Granger-cause n
data: VAR object var2.p
F-Test = 0.364, df1 = 1, df2 = 116, p-value = 0.5474
$Instant
H0: No instantaneous causality between: p65 and n
data: VAR object var2.p
Chi-squared = 0.1892, df = 1, p-value = 0.6635
> impulse<-irf(var2.p,impulse="p65",response=c("n"),boot=FALSE)
> plot(impulse)
>
> p60<-J[,14]
> J2<-data.frame(n,p60)
> var2.p<-VAR(J2,p=1,type="const")
> B(var2.p)
n.l1 p60.l1 const
n 0.9477402 -1.432969e-05 0.5863088
p60 33.5159642 9.995020e-01 -156.4685729
警告メッセージ:
Function 'B' is deprecated; use 'Acoef' instead.
See help("vars-deprecated") and help("B-deprecated") for more information.
> causality(var2.p,cause="p60")
$Granger
Granger causality H0: p60 do not Granger-cause n
data: VAR object var2.p
F-Test = 0.3973, df1 = 1, df2 = 116, p-value = 0.5297
$Instant
H0: No instantaneous causality between: p60 and n
data: VAR object var2.p
Chi-squared = 1.4929, df = 1, p-value = 0.2218
> impulse<-irf(var2.p,impulse="p60",response=c("n"),boot=FALSE)
> plot(impulse)
>
> p55<-J[,13]
> J2<-data.frame(n,p55)
> var2.p<-VAR(J2,p=1,type="const")
> B(var2.p)
n.l1 p55.l1 const
n 0.9229312 0.0000048768 0.6906682
p55 59.4894354 0.9564413453 -146.0923330
警告メッセージ:
Function 'B' is deprecated; use 'Acoef' instead.
See help("vars-deprecated") and help("B-deprecated") for more information.
> causality(var2.p,cause="p55")
$Granger
Granger causality H0: p55 do not Granger-cause n
data: VAR object var2.p
F-Test = 0.0391, df1 = 1, df2 = 116, p-value = 0.8435
$Instant
H0: No instantaneous causality between: p55 and n
data: VAR object var2.p
Chi-squared = 2.7008, df = 1, p-value = 0.1003
> impulse<-irf(var2.p,impulse="p55",response=c("n"),boot=FALSE)
> plot(impulse)
>
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