Content

時系列チャート 単位根検定 共和分検定 相互相関関数 ベクトル自己回帰モデル グレンジャー因果 インパルス応答

  • 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] "2019-04-23~2019-08-26"
[1] 90

$DOW30

    ADF test

data:  x
ADF(0) = -1.7396, p-value = 0.7251
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.07367705 


$NIKKEI225

    ADF test

data:  x
ADF(0) = -1.8786, p-value = 0.6571
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.07859004 


$DOW30_Change

    ADF test

data:  x
ADF(0) = -10.353, p-value = 0.000000000001473
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.128242 


$NIKKEI225_Change

    ADF test

data:  x
ADF(0) = -8.6048, p-value = 0.0000000004754
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.9734566
共和分検定
  • ca.po {urca} 
[1] "2019-04-23~2019-08-26"
[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 
-1224.2  -509.5   125.5   458.4  1226.2 

Coefficients:
        Estimate Std. Error t value            Pr(>|t|)    
z[, -1] 1.235223   0.002973   415.5 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 600.3 on 89 degrees of freedom
Multiple R-squared:  0.9995,    Adjusted R-squared:  0.9995 
F-statistic: 1.726e+05 on 1 and 89 DF,  p-value: < 0.00000000000000022


Value of test-statistic is: 8.3816 

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] "2019-04-23~2019-08-26"
[1] 90


VAR Estimation Results:
========================= 
Endogenous variables: DOW30, NIKKEI225 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -1188.599 
Roots of the characteristic polynomial:
0.9191 0.9191
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        0.94455    0.04742  19.920 <0.0000000000000002 ***
NIKKEI225.l1   -0.02909    0.05793  -0.502              0.6169    
const        2069.02080 1165.36922   1.775              0.0794 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 233 on 86 degrees of freedom
Multiple R-Squared: 0.8671, Adjusted R-squared: 0.864 
F-statistic: 280.5 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       0.07948    0.03393   2.343              0.0215 *  
NIKKEI225.l1   0.89182    0.04145  21.514 <0.0000000000000002 ***
const        190.89959  833.83114   0.229              0.8195    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 166.7 on 86 degrees of freedom
Multiple R-Squared: 0.8987, Adjusted R-squared: 0.8963 
F-statistic: 381.4 on 2 and 86 DF,  p-value: < 0.00000000000000022 



Covariance matrix of residuals:
          DOW30 NIKKEI225
DOW30     54272      6796
NIKKEI225  6796     27785

Correlation matrix of residuals:
          DOW30 NIKKEI225
DOW30     1.000     0.175
NIKKEI225 0.175     1.000
[1] "2019-04-23~2019-08-26"
[1] 90


VAR Estimation Results:
========================= 
Endogenous variables: DOW30_Change, NIKKEI225_Change 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -203.423 
Roots of the characteristic polynomial:
0.3781 0.1366
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     -0.15013    0.10913  -1.376    0.173
NIKKEI225_Change.l1  0.12955    0.12442   1.041    0.301
const               -0.02365    0.09554  -0.248    0.805


Residual standard error: 0.8969 on 86 degrees of freedom
Multiple R-Squared: 0.02829,    Adjusted R-squared: 0.005691 
F-statistic: 1.252 on 2 and 86 DF,  p-value: 0.2911 


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      0.50466    0.08418   5.995 0.0000000464 ***
NIKKEI225_Change.l1 -0.09139    0.09597  -0.952        0.344    
const               -0.09212    0.07369  -1.250        0.215    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.6918 on 86 degrees of freedom
Multiple R-Squared: 0.2951, Adjusted R-squared: 0.2787 
F-statistic:    18 on 2 and 86 DF,  p-value: 0.0000002945 



Covariance matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           0.8045           0.1735
NIKKEI225_Change       0.1735           0.4786

Correlation matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           1.0000           0.2796
NIKKEI225_Change       0.2796           1.0000
グレンジャー因果
  • causality {vars}
  • Dow → Nikkei
[1] "2019-04-23~2019-08-26"
[1] 90


    Granger causality H0: DOW30_Change do not Granger-cause NIKKEI225_Change

data:  VAR object var_result
F-Test = 35.942, df1 = 1, df2 = 172, p-value = 0.00000001164
  • Nikkei → Dow
[1] "2019-04-23~2019-08-26"
[1] 90


    Granger causality H0: NIKKEI225_Change do not Granger-cause DOW30_Change

data:  VAR object var_result
F-Test = 1.0841, df1 = 1, df2 = 172, p-value = 0.2993
インパルス応答
  • irf {vars}