Content

時系列チャート

  • 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。


単位根検定・共和分検定

  • CADFtest {CADFtest}
  • ca.po {urca}
単位根検定
[1] "2019-05-10~2019-09-12"
[1] "n=90"

$DOW30

    ADF test

data:  x
ADF(0) = -1.7825, p-value = 0.7048
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.0736528 


$NIKKEI225

    ADF test

data:  x
ADF(0) = -1.5483, p-value = 0.805
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.07242302 


$DOW30_Change

    ADF test

data:  x
ADF(0) = -9.7307, p-value = 0.000000000009647
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.055849 


$NIKKEI225_Change

    ADF test

data:  x
ADF(0) = -9.4728, p-value = 0.00000000002239
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.033889 
共和分検定
[1] "2019-05-10~2019-09-12"
[1] "n=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 
-1148.81  -273.70    73.55   393.96   992.98 

Coefficients:
        Estimate Std. Error t value            Pr(>|t|)    
z[, -1] 1.246303   0.002453     508 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 491.5 on 89 degrees of freedom
Multiple R-squared:  0.9997,    Adjusted R-squared:  0.9997 
F-statistic: 2.581e+05 on 1 and 89 DF,  p-value: < 0.00000000000000022


Value of test-statistic is: 14.112 

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] "2019-05-10~2019-09-12"
[1] "n=90"


VAR Estimation Results:
========================= 
Endogenous variables: DOW30, NIKKEI225 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -1190.034 
Roots of the characteristic polynomial:
0.9149 0.8442
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        0.95839    0.05215  18.376 <0.0000000000000002 ***
NIKKEI225.l1   -0.04117    0.07948  -0.518               0.606    
const        1977.50219 1287.98879   1.535               0.128    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 236.6 on 86 degrees of freedom
Multiple R-Squared: 0.8702, Adjusted R-squared: 0.8672 
F-statistic: 288.2 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        0.12063    0.03700   3.260              0.0016 ** 
NIKKEI225.l1    0.80070    0.05638  14.201 <0.0000000000000002 ***
const        1037.83743  913.73636   1.136              0.2592    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 167.9 on 86 degrees of freedom
Multiple R-Squared: 0.8492, Adjusted R-squared: 0.8457 
F-statistic: 242.2 on 2 and 86 DF,  p-value: < 0.00000000000000022 



Covariance matrix of residuals:
          DOW30 NIKKEI225
DOW30     55993      8261
NIKKEI225  8261     28181

Correlation matrix of residuals:
          DOW30 NIKKEI225
DOW30     1.000     0.208
NIKKEI225 0.208     1.000
[1] "2019-05-10~2019-09-12"
[1] "n=90"


VAR Estimation Results:
========================= 
Endogenous variables: DOW30_Change, NIKKEI225_Change 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -205.76 
Roots of the characteristic polynomial:
0.3807 0.1457
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     -0.11047    0.10838  -1.019    0.311
NIKKEI225_Change.l1  0.12746    0.11644   1.095    0.277
const                0.06143    0.09671   0.635    0.527


Residual standard error: 0.9103 on 86 degrees of freedom
Multiple R-Squared: 0.02154,    Adjusted R-squared: -0.001213 
F-statistic: 0.9467 on 2 and 86 DF,  p-value: 0.392 


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      0.543214   0.084023   6.465 0.00000000588 ***
NIKKEI225_Change.l1 -0.124549   0.090270  -1.380         0.171    
const               -0.005501   0.074972  -0.073         0.942    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.7058 on 86 degrees of freedom
Multiple R-Squared: 0.3273, Adjusted R-squared: 0.3116 
F-statistic: 20.92 on 2 and 86 DF,  p-value: 0.00000003953 



Covariance matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           0.8287           0.1968
NIKKEI225_Change       0.1968           0.4981

Correlation matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           1.0000           0.3063
NIKKEI225_Change       0.3063           1.0000

グレンジャー因果
  • causality {vars}
Dow → Nikkei
[1] "2019-05-10~2019-09-12"
[1] "n=90"


    Granger causality H0: DOW30_Change do not Granger-cause NIKKEI225_Change

data:  VAR object var_result
F-Test = 41.797, df1 = 1, df2 = 172, p-value = 0.000000001008
Nikkei → Dow
[1] "2019-05-10~2019-09-12"
[1] "n=90"


    Granger causality H0: NIKKEI225_Change do not Granger-cause DOW30_Change

data:  VAR object var_result
F-Test = 1.1983, df1 = 1, df2 = 172, p-value = 0.2752

インパルス応答
  • irf {vars}