Analysis

2019年7月22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

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    MA:25 DeviationRate Close:Diff(lag=1) Close:Ratio(lag=1)
824 2019-06-20 108.11 108.14 107.47 107.68 107.65 104.81      -0.398     0.623 108.9300         -1.15             -0.71             -0.655
825 2019-06-21 107.31 107.53 107.05 107.46 107.10 104.80       0.140     0.448 108.8392         -1.27             -0.22             -0.204
826 2019-06-24 107.31 107.48 107.27 107.42 107.40 104.70       0.103     0.196 108.7312         -1.21             -0.04             -0.037
827 2019-06-25 107.34 107.41 106.78 107.05 107.00 104.93      -0.270     0.590 108.6080         -1.43             -0.37             -0.344
828 2019-06-26 107.18 107.50 107.11 107.46 107.36 104.30       0.261     0.364 108.4916         -0.95              0.41              0.383
829 2019-06-27 107.75 108.15 107.64 108.05 108.08 104.24       0.278     0.474 108.4016         -0.32              0.59              0.549
830 2019-06-28 107.76 107.81 107.57 107.64 107.68 104.11      -0.111     0.223 108.3256         -0.63             -0.41             -0.379
831 2019-07-01 108.38 108.53 108.11 108.33 108.24 103.66      -0.046     0.388 108.2756          0.05              0.69              0.641
832 2019-07-02 108.38 108.47 108.24 108.27 108.42 104.32      -0.101     0.212 108.2296          0.04             -0.06             -0.055
833 2019-07-03 107.84 107.90 107.54 107.75 107.60 104.46      -0.083     0.335 108.1712         -0.39             -0.52             -0.480
834 2019-07-16 107.91 108.10 107.83 108.07 107.95 104.17       0.148     0.250 108.1040         -0.03              0.32              0.297
835 2019-07-17 108.20 108.33 108.12 108.27 108.17 104.43       0.065     0.194 108.0836          0.17              0.20              0.185
836 2019-07-18 107.94 107.97 107.62 107.77 107.70 104.85      -0.157     0.325 108.0644         -0.27             -0.50             -0.462
837 2019-07-19 107.41 107.71 107.22 107.65 107.50 104.61       0.223     0.457 108.0484         -0.37             -0.12             -0.111
838 2019-07-22 107.83 108.07 107.71 107.87 107.96     NA       0.037     0.334 108.0332         -0.15              0.22              0.204
[1] "NIKKEI"
          Date     Open     High      Low    Close CloseToOpen HighToLow    MA:25 DeviationRate Close:Diff(lag=1) Close:Ratio(lag=1)
824 2019-06-20 21417.74 21491.39 21377.27 21462.86       0.211     0.534 21045.23          1.98            128.99              0.605
825 2019-06-21 21487.67 21497.82 21221.70 21258.64      -1.066     1.301 21045.58          1.01           -204.22             -0.952
826 2019-06-24 21223.56 21317.86 21185.67 21285.99       0.294     0.624 21044.95          1.15             27.35              0.129
827 2019-06-25 21238.07 21313.77 21114.47 21193.81      -0.208     0.944 21041.80          0.72            -92.18             -0.433
828 2019-06-26 21067.68 21129.64 21035.84 21086.59       0.090     0.446 21033.93          0.25           -107.22             -0.506
829 2019-06-27 21156.88 21338.17 21123.97 21338.17       0.857     1.014 21041.41          1.41            251.58              1.193
830 2019-06-28 21282.22 21324.93 21199.85 21275.92      -0.030     0.590 21047.76          1.08            -62.25             -0.292
831 2019-07-01 21566.27 21758.34 21559.17 21729.97       0.759     0.924 21069.65          3.13            454.05              2.134
832 2019-07-02 21699.43 21784.22 21697.31 21754.27       0.253     0.401 21089.42          3.15             24.30              0.112
833 2019-07-03 21684.07 21708.72 21566.65 21638.16      -0.212     0.659 21114.81          2.48           -116.11             -0.534
834 2019-07-16 21644.38 21655.52 21514.89 21535.25      -0.504     0.654 21395.37          0.65           -150.65             -0.695
835 2019-07-17 21474.63 21488.27 21380.55 21469.18      -0.025     0.504 21405.97          0.30            -66.07             -0.307
836 2019-07-18 21336.80 21347.84 20993.44 21046.24      -1.362     1.688 21402.63         -1.67           -422.94             -1.970
837 2019-07-19 21146.50 21474.30 21121.90 21466.99       1.516     1.668 21420.03          0.22            420.75              1.999
838 2019-07-22 21394.75 21445.03 21317.85 21416.79       0.103     0.597 21432.03         -0.07            -50.20             -0.234

単位根検定
  • CADFtest {CADFtest}
Analysis period: 2019-04-10 ~ 2019-07-22,60days

$USDJPY_CloseToOpen

    ADF test

data:  x
ADF(0) = -8.4688, p-value = 0.000000009732
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.123136 


$NIKKEI_CloseToOpen

    ADF test

data:  x
ADF(0) = -9.1263, p-value = 0.000000001598
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.207359 

共和分検定
  • ca.po {urca}
Analysis period: 2019-04-10 ~ 2019-07-22,60days


######################################## 
# 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 
-0.42798 -0.12645 -0.02998  0.05326  0.34230 

Coefficients:
        Estimate Std. Error t value Pr(>|t|)    
z[, -1]  0.14208    0.03963   3.585 0.000684 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1585 on 59 degrees of freedom
Multiple R-squared:  0.1789,    Adjusted R-squared:  0.165 
F-statistic: 12.85 on 1 and 59 DF,  p-value: 0.0006837


Value of test-statistic is: 55.4494 

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: 2019-04-10 ~ 2019-07-22,60days


Call:
lm(formula = USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen, data = USDJPY_NIKKEI)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.39323 -0.09038  0.00503  0.09108  0.37200 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)        -0.03621    0.02018  -1.794 0.077973 .  
NIKKEI_CloseToOpen  0.14900    0.03909   3.811 0.000337 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1556 on 58 degrees of freedom
Multiple R-squared:  0.2003,    Adjusted R-squared:  0.1865 
F-statistic: 14.53 on 1 and 58 DF,  p-value: 0.0003366


-----------------------------------------------------------------------------

    Durbin-Watson test

data:  OLS_Model
DW = 2.2138, p-value = 0.8049
alternative hypothesis: true autocorrelation is greater than 0


-----------------------------------------------------------------------------

    One-sample Kolmogorov-Smirnov test

data:  ResidualsOLS
D = 0.079467, p-value = 0.8141
alternative hypothesis: two-sided


-----------------------------------------------------------------------------
                         2.5 %      97.5 %
(Intercept)        -0.07660713 0.004185337
NIKKEI_CloseToOpen  0.07074981 0.227257906

-----------------------------------------------------------------------------

    Box-Ljung test

data:  ResidualsOLS
X-squared = 0.75006, df = 1, p-value = 0.3865
  • 切片項\(=0\)
Analysis period: 2019-04-10 ~ 2019-07-22,60days


Call:
lm(formula = USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen - 1, data = USDJPY_NIKKEI)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.42798 -0.12645 -0.02998  0.05326  0.34230 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
NIKKEI_CloseToOpen  0.14208    0.03963   3.585 0.000684 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1585 on 59 degrees of freedom
Multiple R-squared:  0.1789,    Adjusted R-squared:  0.165 
F-statistic: 12.85 on 1 and 59 DF,  p-value: 0.0006837


-----------------------------------------------------------------------------

    Durbin-Watson test

data:  OLS_Model_no_intercept
DW = 2.0939, p-value = 0.6992
alternative hypothesis: true autocorrelation is greater than 0


-----------------------------------------------------------------------------

    One-sample Kolmogorov-Smirnov test

data:  ResidualsOLS_no_intercept
D = 0.08357, p-value = 0.7646
alternative hypothesis: two-sided


-----------------------------------------------------------------------------
                       2.5 %    97.5 %
NIKKEI_CloseToOpen 0.0627839 0.2213726

-----------------------------------------------------------------------------

    Box-Ljung test

data:  ResidualsOLS_no_intercept
X-squared = 0.71873, df = 1, p-value = 0.3966

一般化最小二乗法
  • 切片項\(\neq0\)
Analysis period: 2019-04-10 ~ 2019-07-22,60days

Generalized least squares fit by REML
  Model: USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen 
  Data: USDJPY_NIKKEI 
        AIC       BIC   logLik
  -38.39366 -32.21233 22.19683

Coefficients:
                        Value  Std.Error   t-value p-value
(Intercept)        -0.0362109 0.02018079 -1.794325  0.0780
NIKKEI_CloseToOpen  0.1490039 0.03909345  3.811478  0.0003

 Correlation: 
                   (Intr)
NIKKEI_CloseToOpen -0.099

Standardized residuals:
        Min          Q1         Med          Q3         Max 
-2.52789372 -0.58101880  0.03235391  0.58552555  2.39141133 

Residual standard error: 0.155556 
Degrees of freedom: 60 total; 58 residual

-----------------------------------------------------------------------------

    One-sample Kolmogorov-Smirnov test

data:  ResidualsGLS
D = 0.079467, p-value = 0.8141
alternative hypothesis: two-sided


-----------------------------------------------------------------------------
                         2.5 %      97.5 %
(Intercept)        -0.07576451 0.003342719
NIKKEI_CloseToOpen  0.07238209 0.225625618

-----------------------------------------------------------------------------

    Box-Ljung test

data:  ResidualsGLS
X-squared = 0.75006, df = 1, p-value = 0.3865
  • 切片項\(=0\)
Analysis period: 2019-04-10 ~ 2019-07-22,60days

Generalized least squares fit by REML
  Model: USDJPY_CloseToOpen ~ NIKKEI_CloseToOpen - 1 
  Data: USDJPY_NIKKEI 
        AIC       BIC   logLik
  -43.18296 -39.02789 23.59148

Coefficients:
                       Value  Std.Error  t-value p-value
NIKKEI_CloseToOpen 0.1420783 0.03962746 3.585349  0.0007

Standardized residuals:
       Min         Q1        Med         Q3        Max 
-2.7009471 -0.7980066 -0.1891916  0.3361123  2.1602626 

Residual standard error: 0.158455 
Degrees of freedom: 60 total; 59 residual

-----------------------------------------------------------------------------

    One-sample Kolmogorov-Smirnov test

data:  ResidualsGLS_no_intercept
D = 0.08357, p-value = 0.7646
alternative hypothesis: two-sided


-----------------------------------------------------------------------------
                        2.5 %    97.5 %
NIKKEI_CloseToOpen 0.06440987 0.2197466

-----------------------------------------------------------------------------

    Box-Ljung test

data:  ResidualsGLS_no_intercept
X-squared = 0.71873, df = 1, p-value = 0.3966

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\(=0\)