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] "2019-03-19~2019-07-22"


$DOW30

    ADF test

data:  x
ADF(0) = -1.408, p-value = 0.852
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.05080072 


$NIKKEI225

    ADF test

data:  x
ADF(0) = -1.9687, p-value = 0.6098
alternative hypothesis: true delta is less than 0
sample estimates:
      delta 
-0.08938536 


$DOW30_Change

    ADF test

data:  x
ADF(0) = -8.9666, p-value = 0.0000000001281
alternative hypothesis: true delta is less than 0
sample estimates:
     delta 
-0.9689877 


$NIKKEI225_Change

    ADF test

data:  x
ADF(0) = -9.9201, p-value = 0.000000000005318
alternative hypothesis: true delta is less than 0
sample estimates:
    delta 
-1.071546
共和分検定
  • ca.po {urca} 
[1] "2019-03-19~2019-07-22"


[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 
-878.8 -472.0 -134.7  473.2 1552.2 

Coefficients:
        Estimate Std. Error t value            Pr(>|t|)    
z[, -1] 1.219731   0.002737   445.6 <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 558.3 on 89 degrees of freedom
Multiple R-squared:  0.9996,    Adjusted R-squared:  0.9995 
F-statistic: 1.986e+05 on 1 and 89 DF,  p-value: < 0.00000000000000022


Value of test-statistic is: 5.6319 

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] "2019-03-19~2019-07-22"



VAR Estimation Results:
========================= 
Endogenous variables: DOW30, NIKKEI225 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -1166.401 
Roots of the characteristic polynomial:
0.9363 0.9363
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        1.00523    0.03802  26.438 <0.0000000000000002 ***
NIKKEI225.l1   -0.09209    0.04755  -1.937              0.0561 .  
const        1857.08200  980.37186   1.894              0.0616 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 173.7 on 86 degrees of freedom
Multiple R-Squared: 0.9128, Adjusted R-squared: 0.9108 
F-statistic: 450.2 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        0.08334    0.03890   2.142               0.035 *  
NIKKEI225.l1    0.86447    0.04865  17.769 <0.0000000000000002 ***
const         727.20505 1003.08518   0.725               0.470    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 177.7 on 86 degrees of freedom
Multiple R-Squared: 0.8534, Adjusted R-squared:  0.85 
F-statistic: 250.3 on 2 and 86 DF,  p-value: < 0.00000000000000022 



Covariance matrix of residuals:
          DOW30 NIKKEI225
DOW30     30166      8061
NIKKEI225  8061     31580

Correlation matrix of residuals:
           DOW30 NIKKEI225
DOW30     1.0000    0.2612
NIKKEI225 0.2612    1.0000
[1] "2019-03-19~2019-07-22"



VAR Estimation Results:
========================= 
Endogenous variables: DOW30_Change, NIKKEI225_Change 
Deterministic variables: const 
Sample size: 89 
Log Likelihood: -185.594 
Roots of the characteristic polynomial:
0.239 0.0376
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     0.022895   0.112709   0.203    0.840
NIKKEI225_Change.l1 0.005721   0.089023   0.064    0.949
const               0.055486   0.073290   0.757    0.451


Residual standard error: 0.6889 on 86 degrees of freedom
Multiple R-Squared: 0.0006742,  Adjusted R-squared: -0.02257 
F-statistic: 0.02901 on 2 and 86 DF,  p-value: 0.9714 


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      0.67313    0.12263   5.489 0.000000402 ***
NIKKEI225_Change.l1 -0.22427    0.09686  -2.315       0.023 *  
const               -0.04162    0.07974  -0.522       0.603    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.7496 on 86 degrees of freedom
Multiple R-Squared: 0.2629, Adjusted R-squared: 0.2458 
F-statistic: 15.34 on 2 and 86 DF,  p-value: 0.00000201 



Covariance matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           0.4746           0.1700
NIKKEI225_Change       0.1700           0.5618

Correlation matrix of residuals:
                 DOW30_Change NIKKEI225_Change
DOW30_Change           1.0000           0.3292
NIKKEI225_Change       0.3292           1.0000
グレンジャー因果
  • causality {vars}
  • Dow → Nikkei
[1] "2019-03-19~2019-07-22"



    Granger causality H0: DOW30_Change do not Granger-cause NIKKEI225_Change

data:  VAR object var_result
F-Test = 30.129, df1 = 1, df2 = 172, p-value = 0.0000001429
  • Nikkei → Dow
[1] "2019-03-19~2019-07-22"



    Granger causality H0: NIKKEI225_Change do not Granger-cause DOW30_Change

data:  VAR object var_result
F-Test = 0.0041306, df1 = 1, df2 = 172, p-value = 0.9488
インパルス応答
  • irf {vars}