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}
$DOW30

    ADF test

data:  x
ADF(0) = -2.3042, p-value = 0.427
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.1088021 


$NIKKEI225

    ADF test

data:  x
ADF(0) = -2.0763, p-value = 0.5514
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.08937778 


$DOW30_Change

    ADF test

data:  x
ADF(0) = -9.5472, p-value = 0.0000000000175
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.038302 


$NIKKEI225_Change

    ADF test

data:  x
ADF(1) = -7.6637, p-value = 0.00000001738
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.179276 

共和分検定
  • ca.po {urca}
[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 
-597.1 -245.5   -7.1  181.8  780.7 

Coefficients:
        Estimate Std. Error t value            Pr(>|t|)    
z[, -1] 1.206778   0.001596   756.3 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 325.2 on 89 degrees of freedom
Multiple R-squared:  0.9998,    Adjusted R-squared:  0.9998 
F-statistic: 5.72e+05 on 1 and 89 DF,  p-value: < 0.00000000000000022


Value of test-statistic is: 17.7745 

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}

VAR Estimation Results:
========================= 
Endogenous variables: DOW30, NIKKEI225 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -1151.48 
Roots of the characteristic polynomial:
0.7935 0.7935
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        0.98161    0.08083  12.145 <0.0000000000000002 ***
NIKKEI225.l1   -0.09140    0.07107  -1.286              0.2019    
const        2447.62849 1201.19248   2.038              0.0447 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 174.4 on 86 degrees of freedom
Multiple R-Squared: 0.8179, Adjusted R-squared: 0.8137 
F-statistic: 193.1 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         0.43279     0.06959   6.219 0.00000001746498335 ***
NIKKEI225.l1     0.60117     0.06119   9.824 0.00000000000000104 ***
const        -2648.05913  1034.25079  -2.560              0.0122 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 150.2 on 86 degrees of freedom
Multiple R-Squared: 0.8957, Adjusted R-squared: 0.8933 
F-statistic: 369.4 on 2 and 86 DF,  p-value: < 0.00000000000000022 



Covariance matrix of residuals:
          DOW30 NIKKEI225
DOW30     30418      7153
NIKKEI225  7153     22550

Correlation matrix of residuals:
           DOW30 NIKKEI225
DOW30     1.0000    0.2731
NIKKEI225 0.2731    1.0000

VAR Estimation Results:
========================= 
Endogenous variables: DOW30_Change, NIKKEI225_Change 
Deterministic variables: const 
Sample size: 85 
Log Likelihood: -154.649 
Roots of the characteristic polynomial:
0.794 0.794 0.7916 0.7916 0.729 0.729 0.7098 0.7098 0.3293 0.1263
Call:
VAR(y = obj, p = selected_lag, type = "const")


Estimation results for equation DOW30_Change: 
============================================= 
DOW30_Change = DOW30_Change.l1 + NIKKEI225_Change.l1 + DOW30_Change.l2 + NIKKEI225_Change.l2 + DOW30_Change.l3 + NIKKEI225_Change.l3 + DOW30_Change.l4 + NIKKEI225_Change.l4 + DOW30_Change.l5 + NIKKEI225_Change.l5 + const 

                     Estimate Std. Error t value Pr(>|t|)   
DOW30_Change.l1     -0.024733   0.120592  -0.205  0.83806   
NIKKEI225_Change.l1 -0.198176   0.122474  -1.618  0.10990   
DOW30_Change.l2      0.147345   0.139978   1.053  0.29593   
NIKKEI225_Change.l2 -0.127995   0.122760  -1.043  0.30051   
DOW30_Change.l3      0.267722   0.143246   1.869  0.06558 . 
NIKKEI225_Change.l3 -0.304716   0.121516  -2.508  0.01435 * 
DOW30_Change.l4      0.410629   0.150693   2.725  0.00802 **
NIKKEI225_Change.l4 -0.130007   0.122370  -1.062  0.29150   
DOW30_Change.l5      0.034324   0.148752   0.231  0.81815   
NIKKEI225_Change.l5 -0.165857   0.088048  -1.884  0.06353 . 
const               -0.003069   0.072837  -0.042  0.96650   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.6644 on 74 degrees of freedom
Multiple R-Squared: 0.1651, Adjusted R-squared: 0.05222 
F-statistic: 1.463 on 10 and 74 DF,  p-value: 0.1707 


Estimation results for equation NIKKEI225_Change: 
================================================= 
NIKKEI225_Change = DOW30_Change.l1 + NIKKEI225_Change.l1 + DOW30_Change.l2 + NIKKEI225_Change.l2 + DOW30_Change.l3 + NIKKEI225_Change.l3 + DOW30_Change.l4 + NIKKEI225_Change.l4 + DOW30_Change.l5 + NIKKEI225_Change.l5 + const 

                     Estimate Std. Error t value     Pr(>|t|)    
DOW30_Change.l1      0.705622   0.119177   5.921 0.0000000932 ***
NIKKEI225_Change.l1 -0.296776   0.121037  -2.452      0.01657 *  
DOW30_Change.l2      0.289534   0.138335   2.093      0.03978 *  
NIKKEI225_Change.l2 -0.326903   0.121319  -2.695      0.00872 ** 
DOW30_Change.l3      0.482771   0.141564   3.410      0.00105 ** 
NIKKEI225_Change.l3 -0.082517   0.120090  -0.687      0.49415    
DOW30_Change.l4      0.190525   0.148924   1.279      0.20477    
NIKKEI225_Change.l4  0.009401   0.120933   0.078      0.93825    
DOW30_Change.l5      0.003742   0.147006   0.025      0.97976    
NIKKEI225_Change.l5 -0.146290   0.087015  -1.681      0.09694 .  
const               -0.030271   0.071982  -0.421      0.67532    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.6566 on 74 degrees of freedom
Multiple R-Squared: 0.4539, Adjusted R-squared: 0.3801 
F-statistic: 6.151 on 10 and 74 DF,  p-value: 0.0000009291 



Covariance matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           0.4415           0.1352
NIKKEI225_Change       0.1352           0.4312

Correlation matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           1.0000           0.3098
NIKKEI225_Change       0.3098           1.0000

グレンジャー因果
  • causality {vars}
  • Dow → Nikkei

    Granger causality H0: DOW30_Change do not Granger-cause NIKKEI225_Change

data:  VAR object var_result
F-Test = 9.9852, df1 = 5, df2 = 148, p-value = 0.00000003003
  • Nikkei → Dow

    Granger causality H0: NIKKEI225_Change do not Granger-cause DOW30_Change

data:  VAR object var_result
F-Test = 1.973, df1 = 5, df2 = 148, p-value = 0.0859

インパルス応答
  • irf {vars}