R help - Mar 2024 - CADFtest difference between max.lag.y with criterion and without criterion

Dear Professor Bernhard,

Sorry for take your time, but I found something strange that I am not able to
explain/understand.

Suppose that I compute the ADF test by using the criterion="BIC" to
select the lags:

summary(CADFtest(y, max.lag.y = 20, type = "drift",
criterion="BIC"))

Suppose that 2 lags are selected.

Next, if I set the lags to 2: summary(CADFtest(y, max.lag.y = 2, type =
"drift"))
the ADF test result is different... You can confirm down, please. I think the
reason is the number of included observations after adjustments... 8533 in the
first case and 8551 in the second case.
What am I doing wrong?
Thank you very much for your help.
Best regards,
Jos? Dias Curto
> summary(CADFtest(y, max.lag.y = 20, type = "drift",
criterion="BIC"))
Augmented DF test
                                            ADF test
t-test statistic:                          0.1070651
p-value:                                   0.9663296
Max lag of the diff. dependent variable:   2.0000000

Call:
dynlm(formula = formula(model), start = obs.1, end = obs.T)

Residuals:
     Min       1Q   Median       3Q      Max
-116.646   -3.719    0.163    4.444  110.891

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)  2.758e-01  2.649e-01   1.041 0.297853
L(y, 1)      2.256e-05  2.107e-04   0.107 0.966330
L(d(y), 1)  -5.086e-02  1.085e-02  -4.689 2.78e-06 ***
L(d(y), 2)  -4.030e-02  1.086e-02  -3.710 0.000209 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Residual standard error: 12.73 on 8529 degrees of freedom
Multiple R-squared:  0.003998, Adjusted R-squared:  0.003648
F-statistic: 17.12 on 2 and 8529 DF,  p-value: 3.809e-08

> summary(CADFtest(y, max.lag.y = 2, type = "drift"))
Augmented DF test

                                           ADF test

t-test statistic:                          0.111863

p-value:                                   0.966685

Max lag of the diff. dependent variable:   2.000000



Call:

dynlm(formula = formula(model), start = obs.1, end = obs.T)



Residuals:

     Min       1Q   Median       3Q      Max

-116.647   -3.706    0.155    4.438  110.890



Coefficients:

              Estimate Std. Error t value Pr(>|t|)

(Intercept)  0.2743714  0.2638699   1.040 0.298463

L(y, 1)      0.0000235  0.0002101   0.112 0.966685

L(d(y), 1)  -0.0508659  0.0108353  -4.694 2.71e-06 ***

L(d(y), 2)  -0.0403022  0.0108507  -3.714 0.000205 ***

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1



Residual standard error: 12.72 on 8547 degrees of freedom

Multiple R-squared:  0.003999, Adjusted R-squared:  0.003649

F-statistic: 17.16 on 2 and 8547 DF,  p-value: 3.662e-08



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