Help me interpret these results:

> # Dickey Fuller Test
> dicky_fuller.trend <- lapply(log_data[, c("log_Spot", "log_Fut", "log_USO", "log_USL", "log_OIL")], 
+                              function(x) ur.df(x, type = "trend", selectlags = "BIC",lags=10))
> 
> dicky_fuller.constant <- lapply(log_data[, c("log_Spot", "log_Fut", "log_USO", "log_USL", "log_OIL")], 
+                                 function(x) ur.df(x, type = "drift", selectlags = "BIC",lags=10))
> 
> dicky_fuller.none <- lapply(log_data[, c("log_Spot", "log_Fut", "log_USO", "log_USL", "log_OIL")], 
+                             function(x) ur.df(x, type = "none", selectlags = "BIC",lags=10))
> 
> lapply(dicky_fuller.trend, summary)
$log_Spot

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.159732 -0.011714 -0.000231  0.011977  0.128919 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  1.414e-02  6.194e-03   2.283   0.0225 *
z.lag.1     -3.567e-03  1.551e-03  -2.300   0.0215 *
tt           7.657e-07  5.923e-07   1.293   0.1962  
z.diff.lag  -2.773e-02  1.820e-02  -1.524   0.1277  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02434 on 3016 degrees of freedom
Multiple R-squared:  0.002625,	Adjusted R-squared:  0.001633 
F-statistic: 2.646 on 3 and 3016 DF,  p-value: 0.04753


Value of test-statistic is: -2.3 1.8013 2.6532 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$log_Fut

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.165787 -0.011823 -0.000195  0.011876  0.129113 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)  1.359e-02  6.151e-03   2.209  0.02723 * 
z.lag.1     -3.426e-03  1.540e-03  -2.225  0.02617 * 
tt           7.391e-07  5.855e-07   1.262  0.20688   
z.diff.lag  -5.567e-02  1.818e-02  -3.062  0.00222 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02399 on 3016 degrees of freedom
Multiple R-squared:  0.004928,	Adjusted R-squared:  0.003939 
F-statistic: 4.979 on 3 and 3016 DF,  p-value: 0.001901


Value of test-statistic is: -2.2248 1.6906 2.483 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$log_USO

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.112390 -0.011693 -0.000745  0.011079  0.110815 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  1.179e-02  5.737e-03   2.055   0.0399 *
z.lag.1     -2.700e-03  1.323e-03  -2.041   0.0413 *
tt           2.012e-06  9.692e-07   2.076   0.0380 *
z.diff.lag  -3.988e-02  1.819e-02  -2.192   0.0285 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02178 on 3016 degrees of freedom
Multiple R-squared:  0.003173,	Adjusted R-squared:  0.002181 
F-statistic:   3.2 on 3 and 3016 DF,  p-value: 0.02243


Value of test-statistic is: -2.0411 2.2622 2.2531 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$log_USL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.087736 -0.009938 -0.000660  0.008945  0.105316 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  8.715e-03  4.107e-03   2.122   0.0339 *
z.lag.1     -2.964e-03  1.397e-03  -2.121   0.0340 *
tt           1.175e-06  6.365e-07   1.847   0.0649 .
z.diff.lag  -3.505e-02  1.820e-02  -1.926   0.0542 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.0186 on 3016 degrees of freedom
Multiple R-squared:  0.00284,	Adjusted R-squared:  0.001848 
F-statistic: 2.864 on 3 and 3016 DF,  p-value: 0.03543


Value of test-statistic is: -2.1211 1.759 2.2864 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$log_OIL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.150840 -0.013202 -0.000832  0.012424  0.182609 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  1.347e-02  6.742e-03   1.998   0.0458 *
z.lag.1     -2.518e-03  1.272e-03  -1.979   0.0479 *
tt           2.209e-06  1.084e-06   2.038   0.0416 *
z.diff.lag  -3.453e-02  1.820e-02  -1.897   0.0579 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02385 on 3016 degrees of freedom
Multiple R-squared:  0.002684,	Adjusted R-squared:  0.001692 
F-statistic: 2.706 on 3 and 3016 DF,  p-value: 0.04383


Value of test-statistic is: -1.979 2.2996 2.1448 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


> lapply(dicky_fuller.constant, summary)
$log_Spot

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.159242 -0.011854 -0.000388  0.012110  0.129484 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)  
(Intercept)  0.010918   0.005672   1.925   0.0543 .
z.lag.1     -0.002536   0.001330  -1.906   0.0567 .
z.diff.lag  -0.028210   0.018202  -1.550   0.1213  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02434 on 3017 degrees of freedom
Multiple R-squared:  0.002072,	Adjusted R-squared:  0.001411 
F-statistic: 3.132 on 2 and 3017 DF,  p-value: 0.04376


Value of test-statistic is: -1.9064 1.866 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$log_Fut

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.164284 -0.011850 -0.000342  0.011765  0.130541 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.010426   0.005618   1.856  0.06357 . 
z.lag.1     -0.002419   0.001317  -1.836  0.06643 . 
z.diff.lag  -0.056137   0.018181  -3.088  0.00204 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02399 on 3017 degrees of freedom
Multiple R-squared:  0.004403,	Adjusted R-squared:  0.003743 
F-statistic: 6.671 on 2 and 3017 DF,  p-value: 0.001286


Value of test-statistic is: -1.8361 1.7386 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$log_USO

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.113691 -0.011974 -0.000826  0.011002  0.112567 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  0.0020477  0.0033011   0.620   0.5351  
z.lag.1     -0.0002745  0.0006208  -0.442   0.6584  
z.diff.lag  -0.0408392  0.0181981  -2.244   0.0249 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02179 on 3017 degrees of freedom
Multiple R-squared:  0.001748,	Adjusted R-squared:  0.001087 
F-statistic: 2.642 on 2 and 3017 DF,  p-value: 0.07139


Value of test-statistic is: -0.4422 1.2367 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$log_USL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.087374 -0.009994 -0.000797  0.008907  0.105821 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  0.0034519  0.0029584   1.167   0.2434  
z.lag.1     -0.0009188  0.0008524  -1.078   0.2812  
z.diff.lag  -0.0359448  0.0181996  -1.975   0.0484 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.0186 on 3017 degrees of freedom
Multiple R-squared:  0.001713,	Adjusted R-squared:  0.001051 
F-statistic: 2.588 on 2 and 3017 DF,  p-value: 0.07531


Value of test-statistic is: -1.0779 0.9327 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$log_OIL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.152212 -0.013303 -0.001054  0.012209  0.184135 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  0.0020745  0.0037711   0.550   0.5823  
z.lag.1     -0.0002144  0.0005850  -0.367   0.7140  
z.diff.lag  -0.0354228  0.0182017  -1.946   0.0517 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02387 on 3017 degrees of freedom
Multiple R-squared:  0.00131,	Adjusted R-squared:  0.0006484 
F-statistic: 1.979 on 2 and 3017 DF,  p-value: 0.1383


Value of test-statistic is: -0.3666 1.3704 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


> lapply(dicky_fuller.none, summary)
$log_Spot

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.160435 -0.011699 -0.000531  0.012103  0.128466 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
z.lag.1     1.687e-05  1.039e-04   0.162    0.871
z.diff.lag -2.949e-02  1.820e-02  -1.621    0.105

Residual standard error: 0.02435 on 3018 degrees of freedom
Multiple R-squared:  0.0008769,	Adjusted R-squared:  0.0002148 
F-statistic: 1.324 on 2 and 3018 DF,  p-value: 0.2661


Value of test-statistic is: 0.1624 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$log_Fut

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.162813 -0.011824 -0.000508  0.011982  0.131849 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
z.lag.1     1.859e-05  1.024e-04   0.182  0.85596   
z.diff.lag -5.736e-02  1.818e-02  -3.156  0.00162 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.024 on 3018 degrees of freedom
Multiple R-squared:  0.003297,	Adjusted R-squared:  0.002637 
F-statistic: 4.992 on 2 and 3018 DF,  p-value: 0.006848


Value of test-statistic is: 0.1815 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$log_USO

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.113403 -0.011927 -0.000777  0.011053  0.112480 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)  
z.lag.1     1.078e-04  7.459e-05   1.445    0.148  
z.diff.lag -4.108e-02  1.819e-02  -2.258    0.024 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02179 on 3018 degrees of freedom
Multiple R-squared:  0.002316,	Adjusted R-squared:  0.001655 
F-statistic: 3.503 on 2 and 3018 DF,  p-value: 0.03022


Value of test-statistic is: 1.4454 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$log_USL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.086912 -0.009934 -0.000850  0.009140  0.105287 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)  
z.lag.1     6.926e-05  9.756e-05   0.710   0.4778  
z.diff.lag -3.646e-02  1.820e-02  -2.004   0.0452 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01861 on 3018 degrees of freedom
Multiple R-squared:  0.001479,	Adjusted R-squared:  0.0008177 
F-statistic: 2.236 on 2 and 3018 DF,  p-value: 0.1071


Value of test-statistic is: 0.7099 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$log_OIL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.151927 -0.013326 -0.000976  0.012170  0.184533 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)  
z.lag.1     1.052e-04  6.739e-05   1.562   0.1185  
z.diff.lag -3.563e-02  1.820e-02  -1.958   0.0503 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02386 on 3018 degrees of freedom
Multiple R-squared:  0.002015,	Adjusted R-squared:  0.001353 
F-statistic: 3.046 on 2 and 3018 DF,  p-value: 0.04768


Value of test-statistic is: 1.5617 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62

> #---------------------
> 
> # Difference Data Dickey Fuller Test
> diff_df.trend <- lapply(diff_log_data[, c("diff_log_Spot", "diff_log_Fut", "diff_log_USO", "diff_log_USL", "diff_log_OIL")], 
+                              function(x) ur.df(x, type = "trend", selectlags = "BIC",lags=10))
> 
> diff_df.constant <- lapply(diff_log_data[, c("diff_log_Spot", "diff_log_Fut", "diff_log_USO", "diff_log_USL", "diff_log_OIL")],
+                                 function(x) ur.df(x, type = "drift", selectlags = "BIC",lags=10))
> 
> diff_df.none <- lapply(diff_log_data[, c("diff_log_Spot", "diff_log_Fut", "diff_log_USO", "diff_log_USL", "diff_log_OIL")], 
+                             function(x) ur.df(x, type = "none", selectlags = "BIC",lags=10))
> 
> lapply(diff_df.trend , summary)
$diff_log_Spot

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.126268 -0.012148  0.000703  0.011754  0.166411 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3.063e-04  8.902e-04  -0.344    0.731    
z.lag.1     -1.048e+00  2.613e-02 -40.114   <2e-16 ***
tt           1.075e-07  5.081e-07   0.212    0.833    
z.diff.lag   1.780e-02  1.821e-02   0.978    0.328    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02433 on 3015 degrees of freedom
Multiple R-squared:  0.5151,	Adjusted R-squared:  0.5146 
F-statistic:  1068 on 3 and 3015 DF,  p-value: < 2.2e-16


Value of test-statistic is: -40.1144 536.3881 804.582 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$diff_log_Fut

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.129356 -0.011718  0.000754  0.011857  0.157915 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3.149e-04  8.772e-04  -0.359    0.720    
z.lag.1     -1.084e+00  2.647e-02 -40.942   <2e-16 ***
tt           1.098e-07  5.006e-07   0.219    0.826    
z.diff.lag   2.487e-02  1.820e-02   1.366    0.172    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02397 on 3015 degrees of freedom
Multiple R-squared:  0.5292,	Adjusted R-squared:  0.5287 
F-statistic:  1130 on 3 and 3015 DF,  p-value: < 2.2e-16


Value of test-statistic is: -40.942 558.7506 838.1258 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$diff_log_USO

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.112036 -0.011069  0.000993  0.011649  0.114697 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.090e-03  7.970e-04  -1.368    0.171    
z.lag.1     -1.042e+00  2.628e-02 -39.640   <2e-16 ***
tt           3.215e-07  4.547e-07   0.707    0.480    
z.diff.lag   2.628e-04  1.821e-02   0.014    0.988    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02177 on 3015 degrees of freedom
Multiple R-squared:  0.5208,	Adjusted R-squared:  0.5203 
F-statistic:  1092 on 3 and 3015 DF,  p-value: < 2.2e-16


Value of test-statistic is: -39.6402 523.7828 785.674 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$diff_log_USL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.106346 -0.009063  0.000927  0.009864  0.085268 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -5.056e-04  6.803e-04  -0.743    0.457    
z.lag.1     -1.021e+00  2.622e-02 -38.949   <2e-16 ***
tt           1.486e-07  3.882e-07   0.383    0.702    
z.diff.lag  -1.495e-02  1.821e-02  -0.821    0.412    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01859 on 3015 degrees of freedom
Multiple R-squared:  0.5185,	Adjusted R-squared:  0.518 
F-statistic:  1082 on 3 and 3015 DF,  p-value: < 2.2e-16


Value of test-statistic is: -38.9486 505.6639 758.4958 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


$diff_log_OIL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.186891 -0.012354  0.001074  0.013238  0.154193 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.227e-03  8.729e-04  -1.406    0.160    
z.lag.1     -1.016e+00  2.620e-02 -38.775   <2e-16 ***
tt           3.554e-07  4.980e-07   0.714    0.475    
z.diff.lag  -1.911e-02  1.821e-02  -1.050    0.294    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02384 on 3015 degrees of freedom
Multiple R-squared:  0.5182,	Adjusted R-squared:  0.5177 
F-statistic:  1081 on 3 and 3015 DF,  p-value: < 2.2e-16


Value of test-statistic is: -38.7747 501.1594 751.7389 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.96 -3.41 -3.12
phi2  6.09  4.68  4.03
phi3  8.27  6.25  5.34


> lapply(diff_df.constant, summary)
$diff_log_Spot

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.126403 -0.012101  0.000705  0.011760  0.166268 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.0001430  0.0004427  -0.323    0.747    
z.lag.1     -1.0480640  0.0261231 -40.120   <2e-16 ***
z.diff.lag   0.0177914  0.0182028   0.977    0.328    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02432 on 3016 degrees of freedom
Multiple R-squared:  0.5151,	Adjusted R-squared:  0.5148 
F-statistic:  1602 on 2 and 3016 DF,  p-value: < 2.2e-16


Value of test-statistic is: -40.1202 804.8147 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$diff_log_Fut

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.129494 -0.011680  0.000767  0.011865  0.157779 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.0001480  0.0004363  -0.339    0.735    
z.lag.1     -1.0839038  0.0264703 -40.948   <2e-16 ***
z.diff.lag   0.0248579  0.0182002   1.366    0.172    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02397 on 3016 degrees of freedom
Multiple R-squared:  0.5292,	Adjusted R-squared:  0.5289 
F-statistic:  1695 on 2 and 3016 DF,  p-value: < 2.2e-16


Value of test-statistic is: -40.9479 838.3664 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$diff_log_USO

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.112445 -0.011083  0.001028  0.011768  0.115162 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.0006015  0.0003964  -1.517    0.129    
z.lag.1     -1.0413269  0.0262714 -39.637   <2e-16 ***
z.diff.lag   0.0001055  0.0182053   0.006    0.995    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02177 on 3016 degrees of freedom
Multiple R-squared:  0.5207,	Adjusted R-squared:  0.5204 
F-statistic:  1638 on 2 and 3016 DF,  p-value: < 2.2e-16


Value of test-statistic is: -39.6372 785.5545 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$diff_log_USL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.106562 -0.009053  0.000923  0.009893  0.085330 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.0002797  0.0003384  -0.827    0.409    
z.lag.1     -1.0210541  0.0262130 -38.952   <2e-16 ***
z.diff.lag  -0.0149917  0.0182052  -0.823    0.410    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01859 on 3016 degrees of freedom
Multiple R-squared:  0.5185,	Adjusted R-squared:  0.5181 
F-statistic:  1624 on 2 and 3016 DF,  p-value: < 2.2e-16


Value of test-statistic is: -38.9522 758.6373 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


$diff_log_OIL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression drift 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.186703 -0.012348  0.001095  0.013238  0.154708 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.0006869  0.0004342  -1.582    0.114    
z.lag.1     -1.0156994  0.0261972 -38.771   <2e-16 ***
z.diff.lag  -0.0192767  0.0182026  -1.059    0.290    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02384 on 3016 degrees of freedom
Multiple R-squared:  0.5181,	Adjusted R-squared:  0.5178 
F-statistic:  1621 on 2 and 3016 DF,  p-value: < 2.2e-16


Value of test-statistic is: -38.7713 751.6067 

Critical values for test statistics: 
      1pct  5pct 10pct
tau2 -3.43 -2.86 -2.57
phi1  6.43  4.59  3.78


> lapply(diff_df.none, summary)
$diff_log_Spot

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.126547 -0.012244  0.000562  0.011618  0.166123 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
z.lag.1    -1.04800    0.02612 -40.125   <2e-16 ***
z.diff.lag  0.01776    0.01820   0.976    0.329    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02432 on 3017 degrees of freedom
Multiple R-squared:  0.5151,	Adjusted R-squared:  0.5148 
F-statistic:  1602 on 2 and 3017 DF,  p-value: < 2.2e-16


Value of test-statistic is: -40.1248 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$diff_log_Fut

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.129643 -0.011827  0.000618  0.011717  0.157637 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
z.lag.1    -1.08383    0.02647 -40.953   <2e-16 ***
z.diff.lag  0.02482    0.01820   1.364    0.173    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02397 on 3017 degrees of freedom
Multiple R-squared:  0.5292,	Adjusted R-squared:  0.5289 
F-statistic:  1695 on 2 and 3017 DF,  p-value: < 2.2e-16


Value of test-statistic is: -40.9525 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$diff_log_USO

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.11308 -0.01169  0.00046  0.01118  0.11458 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
z.lag.1    -1.039821   0.026258 -39.600   <2e-16 ***
z.diff.lag -0.000648   0.018202  -0.036    0.972    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02177 on 3017 degrees of freedom
Multiple R-squared:  0.5203,	Adjusted R-squared:   0.52 
F-statistic:  1636 on 2 and 3017 DF,  p-value: < 2.2e-16


Value of test-statistic is: -39.5996 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$diff_log_USL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.106840 -0.009330  0.000641  0.009618  0.085044 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
z.lag.1    -1.02060    0.02621 -38.945   <2e-16 ***
z.diff.lag -0.01522    0.01820  -0.836    0.403    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01859 on 3017 degrees of freedom
Multiple R-squared:  0.5183,	Adjusted R-squared:  0.518 
F-statistic:  1623 on 2 and 3017 DF,  p-value: < 2.2e-16


Value of test-statistic is: -38.9455 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62


$diff_log_OIL

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression none 


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.187375 -0.013014  0.000405  0.012556  0.154043 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
z.lag.1    -1.01403    0.02618 -38.729   <2e-16 ***
z.diff.lag -0.02011    0.01820  -1.105    0.269    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02385 on 3017 degrees of freedom
Multiple R-squared:  0.5177,	Adjusted R-squared:  0.5174 
F-statistic:  1619 on 2 and 3017 DF,  p-value: < 2.2e-16


Value of test-statistic is: -38.7294 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62