What is the CADF test criterion="BIC" report?

5 messages · Pfaff, Bernhard Dr., Claudio Lupi, p99323005 at ntu.edu.tw

Original

1

5

p99323005 at ntu.edu.tw

Sun, Nov 13, 2011 7:34 PM #

Hello:
   I am a rookie in using R. When I used the unit root test in  
"CADFtest", I got the different t-test statistics between using  
criterion="BIC" and no using criterion. But when I checked the result  
with eviews, I find out that no using criterion is correct. Why after  
using criterion="BIC", I got the different result?


Paul

Augmented DF test
                                             ADF test
t-test statistic:                          -1.389086
p-value:                                    0.855681
Max lag of the diff. dependent variable:    1.000000

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

Residuals:
      Min       1Q   Median       3Q      Max
-0.79726 -0.20587 -0.03332  0.23840  0.70460

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.342321  17.435476   1.396    0.167
trnd         0.009959   0.006941   1.435    0.156
L(y, 1)     -0.026068   0.018767  -1.389    0.856
L(d(y), 1)   0.615983   0.092632   6.650 7.18e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3533 on 65 degrees of freedom
Multiple R-squared: 0.413,	Adjusted R-squared: 0.3859
F-statistic:    NA on NA and NA DF,  p-value: NA

Augmented DF test
                                              ADF test
t-test statistic:                          -2.7285715
p-value:                                    0.2282588
Max lag of the diff. dependent variable:    1.0000000

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

Residuals:
      Min       1Q   Median       3Q      Max
-0.84769 -0.24745 -0.02081  0.24187  0.82344

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 47.661910  17.439021   2.733  0.00776 **
trnd         0.019217   0.007005   2.743  0.00754 **
L(y, 1)     -0.051256   0.018785  -2.729  0.22826
L(d(y), 1)   0.753011   0.075724   9.944 1.61e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3937 on 78 degrees of freedom
Multiple R-squared: 0.5674,	Adjusted R-squared: 0.5508
F-statistic:    NA on NA and NA DF,  p-value: NA

Pfaff, Bernhard Dr.

Mon, Nov 14, 2011 2:12 AM #

Hello Paul,

just a guess: different sample sizes! In your first call, the sample is shorter than in your second. Hence, you can test this, if you curtail your data set in your second call and then you should obtain the same result, i.e.:

Augmented DF test
                                            ADF test
t-test statistic:                          -1.389086
p-value:                                    0.855681
Max lag of the diff. dependent variable:    1.000000

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

Residuals:
     Min       1Q   Median       3Q      Max
-0.79726 -0.20587 -0.03332  0.23840  0.70460

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.471789  17.521147   1.397    0.167
trnd         0.009959   0.006941   1.435    0.156
L(y, 1)     -0.026068   0.018767  -1.389    0.856
L(d(y), 1)   0.615983   0.092632   6.650 7.18e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3533 on 65 degrees of freedom
Multiple R-squared: 0.413,      Adjusted R-squared: 0.3859
F-statistic:    NA on NA and NA DF,  p-value: NA

Though, I am not the package maintainer who could provide you with more insights, but the source code itself.

Best,
Bernhard



-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im Auftrag von p99323005 at ntu.edu.tw
Gesendet: Montag, 14. November 2011 04:35
An: r-help at r-project.org
Betreff: [R] What is the CADF test criterion="BIC" report?

Hello:
   I am a rookie in using R. When I used the unit root test in "CADFtest", I got the different t-test statistics between using criterion="BIC" and no using criterion. But when I checked the result with eviews, I find out that no using criterion is correct. Why after using criterion="BIC", I got the different result?


Paul

Augmented DF test
                                             ADF test
t-test statistic:                          -1.389086
p-value:                                    0.855681
Max lag of the diff. dependent variable:    1.000000

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

Residuals:
      Min       1Q   Median       3Q      Max
-0.79726 -0.20587 -0.03332  0.23840  0.70460

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.342321  17.435476   1.396    0.167
trnd         0.009959   0.006941   1.435    0.156
L(y, 1)     -0.026068   0.018767  -1.389    0.856
L(d(y), 1)   0.615983   0.092632   6.650 7.18e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3533 on 65 degrees of freedom
Multiple R-squared: 0.413,	Adjusted R-squared: 0.3859
F-statistic:    NA on NA and NA DF,  p-value: NA

Augmented DF test
                                              ADF test
t-test statistic:                          -2.7285715
p-value:                                    0.2282588
Max lag of the diff. dependent variable:    1.0000000

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

Residuals:
      Min       1Q   Median       3Q      Max
-0.84769 -0.24745 -0.02081  0.24187  0.82344

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 47.661910  17.439021   2.733  0.00776 **
trnd         0.019217   0.007005   2.743  0.00754 **
L(y, 1)     -0.051256   0.018785  -2.729  0.22826
L(d(y), 1)   0.753011   0.075724   9.944 1.61e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3937 on 78 degrees of freedom
Multiple R-squared: 0.5674,	Adjusted R-squared: 0.5508
F-statistic:    NA on NA and NA DF,  p-value: NA

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Claudio Lupi

Mon, Nov 14, 2011 4:05 AM #

In order for the information criteria to be able to select the model, all the
models have to be estimated on the same sample. Therefore, all the models
are estimated and compared using the same sample used for the model
containing the largest number of lags. You can find this and other details
in
Lupi, C. (2009). "Unit Root CADF Testing with R", Journal of Statistical
Software, 2009, 32(2), 1-19

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p99323005 at ntu.edu.tw

Mon, Nov 14, 2011 10:34 PM #

Hello Bernhard:

Thank you for your kindly help. Actually, I have tried to read the  
source code, but I can not understand it clearly. But with your  
recommendation, I do think you are right.

I guess, when I use the criterion of "BIC" in CADFtest, I set the  
max.lag.y=14. It seems to reduce the sample size. Although "BIC"  
choose the optimal augmented lag=1, but it seems not to use the whole  
sample to re-calculate the ADF-statistics.

If it is true, I think after choosing the optimal augmentd part with  
"BIC", I should run the CADFtest again to avoid the misunderstanding.

Thank you again.

Best,

Paul


?? "Pfaff, Bernhard Dr." <Bernhard_Pfaff at fra.invesco.com>:

Hello Paul,

just a guess: different sample sizes! In your first call, the sample  
is shorter than in your second. Hence, you can test this, if you  
curtail your data set in your second call and then you should obtain  
the same result, i.e.:

library(vars)
data(Canada)
test <- summary(CADFtest(Canada[-c(1:13), 1], max.lag.y = 1))
test

Augmented DF test
                                            ADF test
t-test statistic:                          -1.389086
p-value:                                    0.855681
Max lag of the diff. dependent variable:    1.000000

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

Residuals:
     Min       1Q   Median       3Q      Max
-0.79726 -0.20587 -0.03332  0.23840  0.70460

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.471789  17.521147   1.397    0.167
trnd         0.009959   0.006941   1.435    0.156
L(y, 1)     -0.026068   0.018767  -1.389    0.856
L(d(y), 1)   0.615983   0.092632   6.650 7.18e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3533 on 65 degrees of freedom
Multiple R-squared: 0.413,      Adjusted R-squared: 0.3859
F-statistic:    NA on NA and NA DF,  p-value: NA

Though, I am not the package maintainer who could provide you with  
more insights, but the source code itself.

Best,
Bernhard



-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org  
[mailto:r-help-bounces at r-project.org] Im Auftrag von  
p99323005 at ntu.edu.tw
Gesendet: Montag, 14. November 2011 04:35
An: r-help at r-project.org
Betreff: [R] What is the CADF test criterion="BIC" report?

Hello:
   I am a rookie in using R. When I used the unit root test in  
"CADFtest", I got the different t-test statistics between using  
criterion="BIC" and no using criterion. But when I checked the  
result with eviews, I find out that no using criterion is correct.  
Why after using criterion="BIC", I got the different result?


Paul

data(Canada)

ADFt <- CADFtest(Canada[,1], max.lag.y = 14, criterion="BIC")

summary(ADFt)

Augmented DF test
                                             ADF test
t-test statistic:                          -1.389086
p-value:                                    0.855681
Max lag of the diff. dependent variable:    1.000000

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

Residuals:
      Min       1Q   Median       3Q      Max
-0.79726 -0.20587 -0.03332  0.23840  0.70460

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.342321  17.435476   1.396    0.167
trnd         0.009959   0.006941   1.435    0.156
L(y, 1)     -0.026068   0.018767  -1.389    0.856
L(d(y), 1)   0.615983   0.092632   6.650 7.18e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3533 on 65 degrees of freedom
Multiple R-squared: 0.413,	Adjusted R-squared: 0.3859
F-statistic:    NA on NA and NA DF,  p-value: NA

ADFt1 <- CADFtest(Canada[,1], max.lag.y =1)

summary(ADFt1)

Augmented DF test
                                              ADF test
t-test statistic:                          -2.7285715
p-value:                                    0.2282588
Max lag of the diff. dependent variable:    1.0000000

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

Residuals:
      Min       1Q   Median       3Q      Max
-0.84769 -0.24745 -0.02081  0.24187  0.82344

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 47.661910  17.439021   2.733  0.00776 **
trnd         0.019217   0.007005   2.743  0.00754 **
L(y, 1)     -0.051256   0.018785  -2.729  0.22826
L(d(y), 1)   0.753011   0.075724   9.944 1.61e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3937 on 78 degrees of freedom
Multiple R-squared: 0.5674,	Adjusted R-squared: 0.5508
F-statistic:    NA on NA and NA DF,  p-value: NA

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Claudio Lupi

Tue, Nov 15, 2011 12:08 AM #

Hi Paul,
You are right. Model selection takes places using the common data sample
across ALL checked models (otherwise you would end up comparing models
estimated on different data!). What the procedure returns are the results
based on the common sample. If you want to have the full-sample results, you
should re-run the model using the selected lags (fixed).
Best,
Claudio


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