Content

  • Source:Yahoo Finance,FRED,日本経済新聞社
  • (注意) 欠損値(休場日)は原系列にスプライン補間を掛けた上で前日比を算出している。
時系列チャート

単位根検定
  • CADFtest {CADFtest}
[1] "2019-04-22~2019-08-23"
[1] 90

$DOW30

    ADF test

data:  x
ADF(0) = -1.6036, p-value = 0.7837
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.0683275 


$NIKKEI225

    ADF test

data:  x
ADF(0) = -1.9308, p-value = 0.6299
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.07741138 


$DOW30_Change

    ADF test

data:  x
ADF(0) = -9.6937, p-value = 0.00000000001086
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.096907 


$NIKKEI225_Change

    ADF test

data:  x
ADF(0) = -8.7742, p-value = 0.0000000002557
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.9579853 

共和分検定
  • ca.po {urca}
[1] "2019-04-22~2019-08-23"
[1] 90

[1] "DOW30 × NIKKEI225"

######################################## 
# 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 
-1203.2  -501.8   142.6   470.7  1245.9 

Coefficients:
        Estimate Std. Error t value            Pr(>|t|)    
z[, -1] 1.234284   0.002973   415.1 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 601 on 89 degrees of freedom
Multiple R-squared:  0.9995,    Adjusted R-squared:  0.9995 
F-statistic: 1.723e+05 on 1 and 89 DF,  p-value: < 0.00000000000000022


Value of test-statistic is: 8.6255 

Critical values of Pu are:
                  10pct    5pct    1pct
critical values 20.3933 25.9711 38.3413

相互相関関数
  • ggCcf {forecast}


ベクトル自己回帰モデル
  • VARselect {vars}
  • VAR {vars}
[1] "2019-04-22~2019-08-23"
[1] 90


VAR Estimation Results:
========================= 
Endogenous variables: DOW30, NIKKEI225 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -1184.179 
Roots of the characteristic polynomial:
0.918 0.918
Call:
VAR(y = obj, p = selected_lag, type = "const")


Estimation results for equation DOW30: 
====================================== 
DOW30 = DOW30.l1 + NIKKEI225.l1 + const 

               Estimate Std. Error t value            Pr(>|t|)    
DOW30.l1        0.94402    0.04724  19.982 <0.0000000000000002 ***
NIKKEI225.l1   -0.01585    0.05679  -0.279               0.781    
const        1800.40457 1165.14919   1.545               0.126    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 232.5 on 86 degrees of freedom
Multiple R-Squared: 0.8675, Adjusted R-squared: 0.8644 
F-statistic: 281.5 on 2 and 86 DF,  p-value: < 0.00000000000000022 


Estimation results for equation NIKKEI225: 
========================================== 
NIKKEI225 = DOW30.l1 + NIKKEI225.l1 + const 

              Estimate Std. Error t value            Pr(>|t|)    
DOW30.l1       0.07196    0.03260   2.207               0.030 *  
NIKKEI225.l1   0.89152    0.03919  22.751 <0.0000000000000002 ***
const        401.60948  804.02870   0.499               0.619    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 160.5 on 86 degrees of freedom
Multiple R-Squared: 0.9058, Adjusted R-squared: 0.9036 
F-statistic: 413.5 on 2 and 86 DF,  p-value: < 0.00000000000000022 



Covariance matrix of residuals:
          DOW30 NIKKEI225
DOW30     54071      8289
NIKKEI225  8289     25748

Correlation matrix of residuals:
           DOW30 NIKKEI225
DOW30     1.0000    0.2221
NIKKEI225 0.2221    1.0000
[1] "2019-04-22~2019-08-23"
[1] 90


VAR Estimation Results:
========================= 
Endogenous variables: DOW30_Change, NIKKEI225_Change 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -202.032 
Roots of the characteristic polynomial:
0.3365 0.1384
Call:
VAR(y = obj, p = selected_lag, type = "const")


Estimation results for equation DOW30_Change: 
============================================= 
DOW30_Change = DOW30_Change.l1 + NIKKEI225_Change.l1 + const 

                    Estimate Std. Error t value Pr(>|t|)
DOW30_Change.l1     -0.12392    0.11426  -1.085    0.281
NIKKEI225_Change.l1  0.11865    0.12527   0.947    0.346
const               -0.02561    0.09545  -0.268    0.789


Residual standard error: 0.8957 on 86 degrees of freedom
Multiple R-Squared: 0.01931,    Adjusted R-squared: -0.003496 
F-statistic: 0.8467 on 2 and 86 DF,  p-value: 0.4324 


Estimation results for equation NIKKEI225_Change: 
================================================= 
NIKKEI225_Change = DOW30_Change.l1 + NIKKEI225_Change.l1 + const 

                    Estimate Std. Error t value    Pr(>|t|)    
DOW30_Change.l1      0.46999    0.08749   5.372 0.000000655 ***
NIKKEI225_Change.l1 -0.07426    0.09592  -0.774       0.441    
const               -0.07797    0.07309  -1.067       0.289    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.6859 on 86 degrees of freedom
Multiple R-Squared: 0.2526, Adjusted R-squared: 0.2353 
F-statistic: 14.54 on 2 and 86 DF,  p-value: 0.000003644 



Covariance matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           0.8023           0.1828
NIKKEI225_Change       0.1828           0.4704

Correlation matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           1.0000           0.2975
NIKKEI225_Change       0.2975           1.0000

グレンジャー因果
  • causality {vars}
  • Dow → Nikkei
[1] "2019-04-22~2019-08-23"
[1] 90


    Granger causality H0: DOW30_Change do not Granger-cause NIKKEI225_Change

data:  VAR object var_result
F-Test = 28.86, df1 = 1, df2 = 172, p-value = 0.0000002499
  • Nikkei → Dow
[1] "2019-04-22~2019-08-23"
[1] 90


    Granger causality H0: NIKKEI225_Change do not Granger-cause DOW30_Change

data:  VAR object var_result
F-Test = 0.89711, df1 = 1, df2 = 172, p-value = 0.3449

インパルス応答
  • irf {vars}