Content
head(USDJPY)
cat("------------------------\n")
tail(USDJPY)
cat("------------------------\n")
ts_data <- USDJPY$`USD/JPY`
ts_data
cat("------------------------\n")
diff_ts_data <- diff(ts_data)
diff_ts_data
cat("------------------------\n")
length(diff_ts_data)
Date USD/JPY
1 2017-05-01 112.2436
2 2017-06-01 110.9141
3 2017-07-01 112.4170
4 2017-08-01 109.8270
5 2017-09-01 110.7760
6 2017-10-01 112.9148
------------------------
Date USD/JPY
19 2018-11-01 113.3380
20 2018-12-01 112.1994
21 2019-01-01 108.9605
22 2019-02-01 110.4400
23 2019-03-01 111.1443
24 2019-04-01 111.6073
------------------------
[1] 112.2436 110.9141 112.4170 109.8270 110.7760 112.9148 112.8190 112.9405 110.8710 107.9700 106.0468 107.6562 109.6882 110.0638 111.5210 110.9965 112.0974 112.7218 113.3380 112.1994 108.9605 110.4400 111.1443 111.6073
------------------------
[1] -1.3295 1.5029 -2.5900 0.9490 2.1388 -0.0958 0.1215 -2.0695 -2.9010 -1.9232 1.6094 2.0320 0.3756 1.4572 -0.5245 1.1009 0.6244 0.6162 -1.1386 -3.2389 1.4795 0.7043 0.4630
------------------------
[1] 23
# ここではラグを2次まで取ります。
lag <- 2
# 自己回帰でお世話になるembed{stats}
M_diff <- embed(x = diff_ts_data, dimension = lag + 1)
M_diff
[,1] [,2] [,3]
[1,] -2.5900 1.5029 -1.3295
[2,] 0.9490 -2.5900 1.5029
[3,] 2.1388 0.9490 -2.5900
[4,] -0.0958 2.1388 0.9490
[5,] 0.1215 -0.0958 2.1388
[6,] -2.0695 0.1215 -0.0958
[7,] -2.9010 -2.0695 0.1215
[8,] -1.9232 -2.9010 -2.0695
[9,] 1.6094 -1.9232 -2.9010
[10,] 2.0320 1.6094 -1.9232
[11,] 0.3756 2.0320 1.6094
[12,] 1.4572 0.3756 2.0320
[13,] -0.5245 1.4572 0.3756
[14,] 1.1009 -0.5245 1.4572
[15,] 0.6244 1.1009 -0.5245
[16,] 0.6162 0.6244 1.1009
[17,] -1.1386 0.6162 0.6244
[18,] -3.2389 -1.1386 0.6162
[19,] 1.4795 -3.2389 -1.1386
[20,] 0.7043 1.4795 -3.2389
[21,] 0.4630 0.7043 1.4795
# 原系列からラグ分を除くための添字の作成(トレンド項(linear trend)として流用)
trend_term <- c((lag + 1):(length(ts_data) - 1))
trend_term
[1] 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
# 始めにトレンド項、ドリフト項(constant、定数項)ともに含む場合
result_lm <- summary(lm(M_diff[, 1] ~ ts_data[trend_term] + M_diff[, 2] + M_diff[, 3] + trend_term))
result_lm
cat("------------------------\n")
# ADF検定統計量 = 自己回帰係数(ここではts_dataの係数γ)のt値(但しt分布には従わない)
result_lm$coefficient[2, 1]/result_lm$coefficient[2, 2]
cat("------------------------\n")
# Rには拡張ディッキー＝フラー検定関数としてCADFtest{CADFtest}があります
result_adftest <- CADFtest(model = ts_data, max.lag.y = lag, type = "trend")
result_adftest
cat("------------------------\n")
result_adftest %>>% (statistic)
Call:
lm(formula = M_diff[, 1] ~ ts_data[trend_term] + M_diff[, 2] +
M_diff[, 3] + trend_term)
Residuals:
Min 1Q Median 3Q Max
-2.2350 -0.8228 0.1731 1.0604 2.5038
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 67.26657 23.97459 2.806 0.0127 *
ts_data[trend_term] -0.61067 0.21598 -2.828 0.0121 *
M_diff[, 2] 0.41852 0.21915 1.910 0.0743 .
M_diff[, 3] 0.20474 0.22639 0.904 0.3792
trend_term 0.02984 0.05305 0.562 0.5816
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.47 on 16 degrees of freedom
Multiple R-squared: 0.3658, Adjusted R-squared: 0.2073
F-statistic: 2.307 on 4 and 16 DF, p-value: 0.1028
------------------------
[1] -2.827502
------------------------
ADF test
data: ts_data
ADF(2) = -2.8275, p-value = 0.2036
alternative hypothesis: true delta is less than 0
sample estimates:
delta
-0.6106707
------------------------
ADF(2)
-2.827502
# 続いてドリフト項を含みトレンド項は含まない場合(ドリフト付きランダムウォークモデル仮定)
result_lm <- summary(lm(M_diff[, 1] ~ ts_data[trend_term] + M_diff[, 2] + M_diff[, 3]))
result_lm
cat("------------------------\n")
result_lm$coefficient[2, 1]/result_lm$coefficient[2, 2]
cat("------------------------\n")
result_adftest <- CADFtest(model = ts_data, max.lag.y = lag, type = "drift")
result_adftest
cat("------------------------\n")
result_adftest %>>% (statistic)
Call:
lm(formula = M_diff[, 1] ~ ts_data[trend_term] + M_diff[, 2] +
M_diff[, 3])
Residuals:
Min 1Q Median 3Q Max
-2.0230 -0.7796 0.1067 1.0745 2.2787
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 67.9926 23.4535 2.899 0.00998 **
ts_data[trend_term] -0.6137 0.2115 -2.901 0.00993 **
M_diff[, 2] 0.4217 0.2146 1.965 0.06600 .
M_diff[, 3] 0.2114 0.2215 0.955 0.35318
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.44 on 17 degrees of freedom
Multiple R-squared: 0.3533, Adjusted R-squared: 0.2391
F-statistic: 3.095 on 3 and 17 DF, p-value: 0.05471
------------------------
[1] -2.90144
------------------------
ADF test
data: ts_data
ADF(2) = -2.9014, p-value = 0.06203
alternative hypothesis: true delta is less than 0
sample estimates:
delta
-0.6137171
------------------------
ADF(2)
-2.90144
# 最後にトレンド項、ドリフト項ともに含まない場合(ランダムウォークモデル仮定)
result_lm <- summary(lm(M_diff[, 1] ~ ts_data[trend_term] + M_diff[, 2] + M_diff[, 3] - 1))
result_lm
cat("------------------------\n")
result_lm$coefficient[1, 1]/result_lm$coefficient[1, 2]
cat("------------------------\n")
result_adftest <- CADFtest(model = ts_data, max.lag.y = lag, type = "none")
result_adftest
cat("------------------------\n")
result_adftest %>>% (statistic)
Call:
lm(formula = M_diff[, 1] ~ ts_data[trend_term] + M_diff[, 2] +
M_diff[, 3] - 1)
Residuals:
Min 1Q Median 3Q Max
-2.9382 -1.0912 0.4493 1.5630 1.8780
Coefficients:
Estimate Std. Error t value Pr(>|t|)
ts_data[trend_term] -0.0005631 0.0033713 -0.167 0.869
M_diff[, 2] 0.1452452 0.2284271 0.636 0.533
M_diff[, 3] -0.1170646 0.2260907 -0.518 0.611
Residual standard error: 1.711 on 18 degrees of freedom
Multiple R-squared: 0.03409, Adjusted R-squared: -0.1269
F-statistic: 0.2117 on 3 and 18 DF, p-value: 0.8869
------------------------
[1] -0.1670245
------------------------
ADF test
data: ts_data
ADF(2) = -0.16702, p-value = 0.614
alternative hypothesis: true delta is less than 0
sample estimates:
delta
-0.0005630961
------------------------
ADF(2)
-0.1670245
\[ \Delta y_{t}= \alpha + \beta t + \gamma y_{t-1} + \delta_{1} \Delta y_{t-1}+ \delta_{2} \Delta y_{t-2} + \epsilon_{t} \]