『経済・ファイナンスデータの計量時系列分析』

の章末問題で「コンピュータを用いて」とあるものをRで解いています。

サポートサイト（データダウンロード）

5.2.

data<-read.table("economicdata.txt",header=T)
data.ts<-ts(data=data[,2:7],start=c(1975, 1), frequency=12)

以下すべてトレンドがあるので「場合3」の筈だが、解答例と異なる

topix

plot(stl(data.ts[,1], s.window="per"), main="topix")

exrate

plot(stl(data.ts[,2], s.window="per"), main="exrate")

indprod(本書ではGDP)

plot(stl(data.ts[,3], s.window="per"), main="indprod(GDP)")

plot(stl(data.ts[,4], s.window="per"), main="cpi")

saunemp(失業率)

plot(stl(data.ts[,5], s.window="per"), main="saunemp")

intrate(コールレート)

plot(stl(data.ts[,6], s.window="per"), main="intrate")

5.3.

テキストの値と合わないが、差分を取って帰無仮説が棄却されたので、単位根過程
-- 差分系列で分析を行う

library(tseries)
adf.test(data.ts[,5],alternative="stationary")

	Augmented Dickey-Fuller Test

data:  data.ts[, 5]
Dickey-Fuller = -1.5663, Lag order = 7, p-value = 0.76
alternative hypothesis: stationary

adf.test(data.ts[,5],alternative="explosive")

	Augmented Dickey-Fuller Test

data:  data.ts[, 5]
Dickey-Fuller = -1.5663, Lag order = 7, p-value = 0.24
alternative hypothesis: explosive

adf.test(diff(data.ts[,5]),alternative="stationary")

	Augmented Dickey-Fuller Test

data:  diff(data.ts[, 5])
Dickey-Fuller = -5.3633, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(data.ts[, 5]), alternative = "stationary") :
  p-value smaller than printed p-value

adf.test(diff(data.ts[,5]),alternative="explosive")

	Augmented Dickey-Fuller Test

data:  diff(data.ts[, 5])
Dickey-Fuller = -5.3633, Lag order = 7, p-value = 0.99
alternative hypothesis: explosive

5.5.

トレンドの有無でalternative=c("stationaly", "explosiv")を指定する必要があるが、以下は"stationaly"で実行

(1)

topix

adf.test(log(data.ts[,1]))

	Augmented Dickey-Fuller Test

data:  log(data.ts[, 1])
Dickey-Fuller = -1.2425, Lag order = 7, p-value = 0.8966
alternative hypothesis: stationary

adf.test(log(data.ts[,1]), alternative="explosiv")

	Augmented Dickey-Fuller Test

data:  log(data.ts[, 1])
Dickey-Fuller = -1.2425, Lag order = 7, p-value = 0.1034
alternative hypothesis: explosive

pp.test(log(data.ts[,1]))

	Phillips-Perron Unit Root Test

data:  log(data.ts[, 1])
Dickey-Fuller Z(alpha) = -2.6978, Truncation lag parameter = 5, p-value =
0.9476
alternative hypothesis: stationary

exrate

adf.test(log(data.ts[,2]))

	Augmented Dickey-Fuller Test

data:  log(data.ts[, 2])
Dickey-Fuller = -1.748, Lag order = 7, p-value = 0.6833
alternative hypothesis: stationary

pp.test(log(data.ts[,2]))

	Phillips-Perron Unit Root Test

data:  log(data.ts[, 2])
Dickey-Fuller Z(alpha) = -7.2163, Truncation lag parameter = 5, p-value =
0.7062
alternative hypothesis: stationary

indprod(本書ではGDP)

adf.test(log(data.ts[,3]))

	Augmented Dickey-Fuller Test

data:  log(data.ts[, 3])
Dickey-Fuller = -2.2418, Lag order = 7, p-value = 0.4749
alternative hypothesis: stationary

pp.test(log(data.ts[,3]))

	Phillips-Perron Unit Root Test

data:  log(data.ts[, 3])
Dickey-Fuller Z(alpha) = -4.6404, Truncation lag parameter = 5, p-value =
0.8504
alternative hypothesis: stationary

adf.test(log(data.ts[,4]))

	Augmented Dickey-Fuller Test

data:  log(data.ts[, 4])
Dickey-Fuller = -3.8057, Lag order = 7, p-value = 0.01899
alternative hypothesis: stationary

pp.test(log(data.ts[,4]))

	Phillips-Perron Unit Root Test

data:  log(data.ts[, 4])
Dickey-Fuller Z(alpha) = -4.1101, Truncation lag parameter = 5, p-value =
0.8801
alternative hypothesis: stationary

saunemp(失業率)

adf.test(data.ts[,5])

	Augmented Dickey-Fuller Test

data:  data.ts[, 5]
Dickey-Fuller = -1.5663, Lag order = 7, p-value = 0.76
alternative hypothesis: stationary

pp.test(data.ts[,5])

	Phillips-Perron Unit Root Test

data:  data.ts[, 5]
Dickey-Fuller Z(alpha) = -3.4958, Truncation lag parameter = 5, p-value =
0.9117
alternative hypothesis: stationary

intrate(コールレート)

adf.test(data.ts[,6])

	Augmented Dickey-Fuller Test

data:  data.ts[, 6]
Dickey-Fuller = -3.7402, Lag order = 7, p-value = 0.02226
alternative hypothesis: stationary

pp.test(data.ts[,6])

	Phillips-Perron Unit Root Test

data:  data.ts[, 6]
Dickey-Fuller Z(alpha) = -15.324, Truncation lag parameter = 5, p-value =
0.2523
alternative hypothesis: stationary

cpi, intrateのadfのみ帰無仮説を棄却

(2)

topix

adf.test(diff(log(data.ts[,1])))

	Augmented Dickey-Fuller Test

data:  diff(log(data.ts[, 1]))
Dickey-Fuller = -6.3141, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(log(data.ts[, 1]))) : p-value smaller than printed p-value

pp.test(diff(log(data.ts[,1])))

	Phillips-Perron Unit Root Test

data:  diff(log(data.ts[, 1]))
Dickey-Fuller Z(alpha) = -253.61, Truncation lag parameter = 5, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In pp.test(diff(log(data.ts[, 1]))) : p-value smaller than printed p-value

exrate

adf.test(diff(log(data.ts[,2])))

	Augmented Dickey-Fuller Test

data:  diff(log(data.ts[, 2]))
Dickey-Fuller = -5.8527, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(log(data.ts[, 2]))) : p-value smaller than printed p-value

pp.test(diff(log(data.ts[,2])))

	Phillips-Perron Unit Root Test

data:  diff(log(data.ts[, 2]))
Dickey-Fuller Z(alpha) = -246.95, Truncation lag parameter = 5, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In pp.test(diff(log(data.ts[, 2]))) : p-value smaller than printed p-value

indprod(本書ではGDP)

adf.test(diff(log(data.ts[,3])))

	Augmented Dickey-Fuller Test

data:  diff(log(data.ts[, 3]))
Dickey-Fuller = -5.1424, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(log(data.ts[, 3]))) : p-value smaller than printed p-value

pp.test(diff(log(data.ts[,3])))

	Phillips-Perron Unit Root Test

data:  diff(log(data.ts[, 3]))
Dickey-Fuller Z(alpha) = -553.4, Truncation lag parameter = 5, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In pp.test(diff(log(data.ts[, 3]))) : p-value smaller than printed p-value

adf.test(diff(log(data.ts[,4])))

	Augmented Dickey-Fuller Test

data:  diff(log(data.ts[, 4]))
Dickey-Fuller = -4.6986, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(log(data.ts[, 4]))) : p-value smaller than printed p-value

pp.test(diff(log(data.ts[,4])))

	Phillips-Perron Unit Root Test

data:  diff(log(data.ts[, 4]))
Dickey-Fuller Z(alpha) = -267.34, Truncation lag parameter = 5, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In pp.test(diff(log(data.ts[, 4]))) : p-value smaller than printed p-value

saunemp(失業率)

adf.test(diff(data.ts[,5]))

	Augmented Dickey-Fuller Test

data:  diff(data.ts[, 5])
Dickey-Fuller = -5.3633, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(data.ts[, 5])) : p-value smaller than printed p-value

pp.test(diff(data.ts[,5]))

	Phillips-Perron Unit Root Test

data:  diff(data.ts[, 5])
Dickey-Fuller Z(alpha) = -387.91, Truncation lag parameter = 5, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In pp.test(diff(data.ts[, 5])) : p-value smaller than printed p-value

intrate(コールレート)

adf.test(diff(data.ts[,6]))

	Augmented Dickey-Fuller Test

data:  diff(data.ts[, 6])
Dickey-Fuller = -5.9193, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(diff(data.ts[, 6])) : p-value smaller than printed p-value

pp.test(diff(data.ts[,6]))

	Phillips-Perron Unit Root Test

data:  diff(data.ts[, 6])
Dickey-Fuller Z(alpha) = -263.86, Truncation lag parameter = 5, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In pp.test(diff(data.ts[, 6])) : p-value smaller than printed p-value

すべて、p-value=0.01 となり、5or1%の危険率で帰無仮説が棄却される。

次は、『経済・ファイナンスデータの計量時系列分析』章末問題をRで解く－第6章見せかけの回帰と共和分－