更新終了:日経平均株価と東京市場ドル円レート
- 日足チャート、移動平均線、単位根検定、共和分検定、最小二乗法、一般化最小二乗法、散布図･QQプロット･残差の時系列推移 -
アセット･マネジメント･コンサルティング株式会社 https://am-consulting.co.jp
更新日時:2019-08-27 05:59:09
Analysis
2019年8月26日の結果
- 日経平均株価の終値対始値比(\(x\))と東京市場ドル円レートの終値対始値比(\(y\))との線形モデル、その回帰係数が\(a\)であった場合(\(y=ax\)、切片は0)、15時時点(大引け時点)の日経平均株価が始値比で仮に1%上昇(下落)したとすると、その2時間後17時点のドル円レートは9時時点のドル円レートより\(a\)%上昇(下落)することを意味します。*終値対始値比:%。分母が始値、分子は終値。
- 過去の解説動画
- Ljung-Box 検定のラグは10としている。
時系列チャート 単位根検定 共和分検定 最小二乗法 一般化最小二乗法 散布図･QQプロット･残差の時系列推移
時系列チャート
[1] "USDJPY"
Date Open High Low Close Center Index CloseToOpen HighToLow MA25 DeviationRate Close:Diff(lag=1) Close:Ratio(lag=1)
855 2019-08-05 106.57 106.68 105.79 105.95 106.03 108.13 -0.582 0.841 108.1252 -2.01 -0.97 -0.907
856 2019-08-06 105.62 107.08 105.52 106.38 105.60 107.39 0.720 1.478 108.0472 -1.54 0.43 0.406
857 2019-08-07 106.33 106.45 105.94 106.30 106.15 107.79 -0.028 0.481 107.9684 -1.55 -0.08 -0.075
858 2019-08-08 106.11 106.32 106.00 106.11 106.11 107.80 0.000 0.302 107.9028 -1.66 -0.19 -0.179
859 2019-08-09 105.89 106.07 105.77 105.95 105.98 108.36 0.057 0.284 107.8284 -1.74 -0.16 -0.151
860 2019-08-13 105.38 105.58 105.13 105.20 105.43 107.17 -0.171 0.428 107.7140 -2.33 -0.75 -0.708
861 2019-08-14 106.61 106.70 106.24 106.45 106.36 108.24 -0.150 0.433 107.6380 -1.10 1.25 1.188
862 2019-08-15 105.92 106.77 105.76 106.25 105.93 108.02 0.312 0.955 107.5352 -1.20 -0.20 -0.188
863 2019-08-16 106.10 106.27 106.03 106.17 106.15 107.78 0.066 0.226 107.4236 -1.17 -0.08 -0.075
864 2019-08-19 106.43 106.47 106.25 106.41 106.38 107.69 -0.019 0.207 107.3576 -0.88 0.24 0.226
865 2019-08-20 106.57 106.69 106.40 106.47 106.56 108.03 -0.094 0.273 107.2816 -0.76 0.06 0.056
866 2019-08-21 106.28 106.60 106.25 106.55 106.47 107.61 0.254 0.329 107.2208 -0.63 0.08 0.075
867 2019-08-22 106.60 106.65 106.30 106.45 106.45 107.98 -0.141 0.329 107.1480 -0.65 -0.10 -0.094
868 2019-08-23 106.47 106.67 106.43 106.65 106.55 109.07 0.169 0.226 107.1032 -0.42 0.20 0.188
869 2019-08-26 104.85 105.95 104.46 105.74 105.25 NA 0.849 1.426 107.0268 -1.20 -0.91 -0.853[1] "NIKKEI"
Date Open High Low Close CloseToOpen HighToLow MA25 DeviationRate Close:Diff(lag=1) Close:Ratio(lag=1)
855 2019-08-05 20909.98 20941.83 20514.19 20720.29 -0.907 2.085 21536.37 -3.79 -366.87 -1.740
856 2019-08-06 20325.52 20607.83 20110.76 20585.31 1.278 2.472 21490.59 -4.21 -134.98 -0.651
857 2019-08-07 20548.07 20570.19 20406.52 20516.56 -0.153 0.802 21441.08 -4.31 -68.75 -0.334
858 2019-08-08 20529.29 20682.24 20462.98 20593.35 0.312 1.071 21399.29 -3.77 76.79 0.374
859 2019-08-09 20758.15 20782.06 20676.92 20684.82 -0.353 0.508 21358.58 -3.15 91.47 0.444
860 2019-08-13 20432.68 20503.38 20369.27 20455.44 0.111 0.658 21306.94 -4.00 -229.38 -1.109
861 2019-08-14 20669.99 20697.42 20581.17 20655.13 -0.072 0.565 21271.77 -2.90 199.69 0.976
862 2019-08-15 20324.25 20419.88 20184.85 20405.65 0.401 1.164 21225.39 -3.86 -249.48 -1.208
863 2019-08-16 20323.97 20465.71 20300.35 20418.81 0.467 0.815 21180.81 -3.60 13.16 0.064
864 2019-08-19 20590.47 20633.90 20502.66 20563.16 -0.133 0.640 21137.59 -2.72 144.35 0.707
865 2019-08-20 20605.35 20684.06 20582.01 20677.22 0.349 0.496 21097.25 -1.99 114.06 0.555
866 2019-08-21 20489.97 20626.05 20482.62 20618.57 0.628 0.700 21060.58 -2.10 -58.65 -0.284
867 2019-08-22 20706.07 20731.19 20584.29 20628.01 -0.377 0.714 21026.93 -1.90 9.44 0.046
868 2019-08-23 20579.98 20719.31 20579.98 20710.91 0.636 0.677 21013.52 -1.44 82.90 0.402
869 2019-08-26 20325.44 20329.01 20173.76 20261.04 -0.317 0.770 20965.28 -3.36 -449.87 -2.172
単位根検定
- CADFtest {CADFtest}
Analysis period: 2019-05-31 ~ 2019-08-26,60days
$USDJPY_CloseToOpen
ADF test
data: x
ADF(1) = -6.9434, p-value = 0.00000121
alternative hypothesis: true delta is less than 0
sample estimates:
delta
-1.533123
$NIKKEI_CloseToOpen
ADF test
data: x
ADF(0) = -10.28, p-value = 0.0000000001205
alternative hypothesis: true delta is less than 0
sample estimates:
delta
-1.328412
共和分検定
- ca.po {urca}
Analysis period: 2019-05-31 ~ 2019-08-26,60days
########################################
# Phillips and Ouliaris Unit Root Test #
########################################
Test of type Pu
detrending of series none
Call:
lm(formula = z[, 1] ~ z[, -1] - 1)
Residuals:
Min 1Q Median 3Q Max
-0.44301 -0.15925 -0.02511 0.07655 0.91662
Coefficients:
Estimate Std. Error t value Pr(>|t|)
z[, -1] 0.21331 0.05369 3.973 0.000196 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2182 on 59 degrees of freedom
Multiple R-squared: 0.211, Adjusted R-squared: 0.1977
F-statistic: 15.78 on 1 and 59 DF, p-value: 0.0001959
Value of test-statistic is: 44.9729
Critical values of Pu are:
10pct 5pct 1pct
critical values 20.3933 25.9711 38.3413
最小二乗法
- lm {stats}
- dwtest {lmtest}
- ks.test {stats}
- confint {stats}
- Box.test {stats}
- 切片項\(\neq0\)
Analysis period: 2019-05-31 ~ 2019-08-26,60days
Call:
lm(formula = USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen, data = USDJPY_NIKKEI)
Residuals:
Min 1Q Median 3Q Max
-0.42027 -0.13520 -0.00275 0.09939 0.94284
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.02413 0.02853 -0.846 0.401116
NIKKEI_CloseToOpen 0.21991 0.05439 4.043 0.000157 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2187 on 58 degrees of freedom
Multiple R-squared: 0.2199, Adjusted R-squared: 0.2065
F-statistic: 16.35 on 1 and 58 DF, p-value: 0.0001573
-----------------------------------------------------------------------------
Durbin-Watson test
data: OLS_Model
DW = 1.6479, p-value = 0.08994
alternative hypothesis: true autocorrelation is greater than 0
-----------------------------------------------------------------------------
One-sample Kolmogorov-Smirnov test
data: ResidualsOLS
D = 0.10308, p-value = 0.5136
alternative hypothesis: two-sided
-----------------------------------------------------------------------------
2.5 % 97.5 %
(Intercept) -0.08123885 0.03297624
NIKKEI_CloseToOpen 0.11104161 0.32877155
-----------------------------------------------------------------------------
Box-Ljung test
data: ResidualsOLS
X-squared = 7.4389, df = 10, p-value = 0.6835- 切片項\(=0\)
Analysis period: 2019-05-31 ~ 2019-08-26,60days
Call:
lm(formula = USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen - 1, data = USDJPY_NIKKEI)
Residuals:
Min 1Q Median 3Q Max
-0.44301 -0.15925 -0.02511 0.07655 0.91662
Coefficients:
Estimate Std. Error t value Pr(>|t|)
NIKKEI_CloseToOpen 0.21331 0.05369 3.973 0.000196 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2182 on 59 degrees of freedom
Multiple R-squared: 0.211, Adjusted R-squared: 0.1977
F-statistic: 15.78 on 1 and 59 DF, p-value: 0.0001959
-----------------------------------------------------------------------------
Durbin-Watson test
data: OLS_Model_no_intercept
DW = 1.6282, p-value = 0.09847
alternative hypothesis: true autocorrelation is greater than 0
-----------------------------------------------------------------------------
One-sample Kolmogorov-Smirnov test
data: ResidualsOLS_no_intercept
D = 0.14298, p-value = 0.1559
alternative hypothesis: two-sided
-----------------------------------------------------------------------------
2.5 % 97.5 %
NIKKEI_CloseToOpen 0.1058675 0.3207477
-----------------------------------------------------------------------------
Box-Ljung test
data: ResidualsOLS_no_intercept
X-squared = 7.5784, df = 10, p-value = 0.6699
一般化最小二乗法
- gls {nlme}
- corARMA {nlme}
- ks.test {stats}
- confint {stats}
- Box.test {stats}
- 残差の系列相関の有無に拘わらず一般化最小二乗法による回帰係数を求めています。
- 最小二乗法の残差に系列相関が見られない場合、ここではAR(p=0,q=0)の結果(AIC最小)が表示されます。
- http://user.keio.ac.jp/~nagakura/zemi/GLS.pdf
- http://tokyox.matrix.jp/wiki/index.php?%E4%B8%80%E8%88%AC%E5%8C%96%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%97%E6%B3%95
- 切片項\(\neq0\)
Analysis period: 2019-05-31 ~ 2019-08-26,60days
Generalized least squares fit by REML
Model: USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen
Data: USDJPY_NIKKEI
AIC BIC logLik
0.8517216 11.15394 4.574139
Correlation Structure: ARMA(1,1)
Formula: ~1
Parameter estimate(s):
Phi1 Theta1
-0.5790455 0.8274226
Coefficients:
Value Std.Error t-value p-value
(Intercept) -0.02279688 0.03149008 -0.723939 0.472
NIKKEI_CloseToOpen 0.21564166 0.04374439 4.929584 0.000
Correlation:
(Intr)
NIKKEI_CloseToOpen -0.093
Standardized residuals:
Min Q1 Med Q3 Max
-1.9149399 -0.6208827 -0.0136277 0.4501184 4.2793579
Residual standard error: 0.2196954
Degrees of freedom: 60 total; 58 residual
-----------------------------------------------------------------------------
One-sample Kolmogorov-Smirnov test
data: ResidualsGLS
D = 0.10344, p-value = 0.5092
alternative hypothesis: two-sided
-----------------------------------------------------------------------------
2.5 % 97.5 %
(Intercept) -0.0845163 0.03892254
NIKKEI_CloseToOpen 0.1299042 0.30137909
-----------------------------------------------------------------------------
Box-Ljung test
data: ResidualsGLS
X-squared = 7.529, df = 10, p-value = 0.6747- 切片項\(=0\)
Analysis period: 2019-05-31 ~ 2019-08-26,60days
Generalized least squares fit by REML
Model: USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen - 1
Data: USDJPY_NIKKEI
AIC BIC logLik
-5.705376 2.604774 6.852688
Correlation Structure: ARMA(1,1)
Formula: ~1
Parameter estimate(s):
Phi1 Theta1
-0.5761774 0.8236721
Coefficients:
Value Std.Error t-value p-value
NIKKEI_CloseToOpen 0.2123643 0.04350093 4.881833 0
Standardized residuals:
Min Q1 Med Q3 Max
-2.0245727 -0.7282230 -0.1135206 0.3508311 4.1895173
Residual standard error: 0.2187172
Degrees of freedom: 60 total; 59 residual
-----------------------------------------------------------------------------
One-sample Kolmogorov-Smirnov test
data: ResidualsGLS_no_intercept
D = 0.14248, p-value = 0.1587
alternative hypothesis: two-sided
-----------------------------------------------------------------------------
2.5 % 97.5 %
NIKKEI_CloseToOpen 0.127104 0.2976245
-----------------------------------------------------------------------------
Box-Ljung test
data: ResidualsGLS_no_intercept
X-squared = 7.5984, df = 10, p-value = 0.668
散布図･QQプロット･残差の時系列推移
- (注意)線形回帰の傾き(\(a\))、切片(\(b\))それぞれの検定統計量、p値に関わらず\(y=ax+b\)とした回帰直線やその残差を散布図、QQプロット等にプロットしています。
- 切片項\(\neq0\)
- 切片項\(=0\)
- 残差の自己相関
