The RATS Software Forum

Dear All,

I want to do the stationarity test for two nostationary variable. I have used the following command.

@adfautoselect(maxlags=14,det=trend,print) lfp (to check the lag of series but is it necessary to check the auto correlation here?)

Then i got the following output

Information Criteria for ADF Lag Lengths, Series LFP
Lags AIC BIC HQ MAIC ADF
0 -8.439 -8.430* -8.436* -8.437 -2.244
1 -8.439 -8.428 -8.435 -8.436 -2.317
2 -8.439 -8.425 -8.434 -8.437 -2.230
3 -8.439* -8.423 -8.433 -8.437* -2.313
4 -8.439 -8.420 -8.432 -8.436 -2.372 (How to interpret this values of AIC, BIC, HQ, MAIC, ADF?)
5 -8.439 -8.417 -8.431 -8.437 -2.291
6 -8.438 -8.413 -8.429 -8.436 -2.262
7 -8.438 -8.410 -8.427 -8.435 -2.294
8 -8.437 -8.406 -8.426 -8.434 -2.317
9 -8.436 -8.403 -8.424 -8.433 -2.348
10 -8.436 -8.399 -8.422 -8.433 -2.294
11 -8.435 -8.396 -8.420 -8.432 -2.265
12 -8.435 -8.393 -8.419 -8.433 -2.190
13 -8.435 -8.390 -8.419 -8.433 -2.113
14 -8.434 -8.387 -8.417 -8.432 -2.153

It shows the autocorrelation problem persists over all the lag including level(0) so if i use the following command

@dfunit(lags=0,det=trend, method=AIC) lfp (is this command correct)

When i run the same command with the first difference @adfautoselect(maxlags=14,det=trend,print) dlfp, I got the output

Information Criteria for ADF Lag Lengths, Series DLFP
Lags AIC BIC HQ MAIC ADF
0 -8.437 -8.429* -8.434* -6.560 -43.547
1 -8.438 -8.426 -8.433 -6.405 -32.536
2 -8.438* -8.424 -8.433 -6.546 -25.416
3 -8.437 -8.421 -8.431 -6.633* -21.592
4 -8.438 -8.418 -8.431 -6.498 -20.169 (AIC, BIC, HQ, MAIC remain almost similar to the level series, how to interpret the result?)
5 -8.437 -8.415 -8.429 -6.443 -18.648
6 -8.436 -8.411 -8.427 -6.493 -16.995
7 -8.435 -8.407 -8.425 -6.526 -15.751
8 -8.434 -8.404 -8.423 -6.570 -14.682
9 -8.434 -8.401 -8.422 -6.477 -14.292
10 -8.433 -8.397 -8.420 -6.425 -13.791
11 -8.433 -8.394 -8.419 -6.279 -13.648
12 -8.434 -8.392 -8.418 -6.119 -13.530
13 -8.433 -8.389 -8.417 -6.200 -12.720
14 -8.433 -8.386 -8.416 -6.334 -11.861

Whether i have to use @dfunit(lags=0,det=trend, method=AIC) dlfp command to check stationarity of the series?

I need your help to understand the topic.

With sincere regards,
Upananda

I think you need to read up on information criteria---see Section 2.9 of the User's Guide. The @ADFAUTOSELECT is not showing that the autocorrelation "persists". The *'s show that BIC and HQ pick 0 lags, while AIC and MAIC pick 4. In each of those, the optimal lag length is the one which minimizes a particular criterion. You don't try to "interpret" the values---you compare them within a column.

The fact that the two @ADFAUTOSELECTs produce fairly similar IC's isn't that much of a surprise given that you appear to have a unit root, since then the AR on the level and AR on the differences will give almost identical fits.

Dear Sir,

Thanks a lot for your reply. As per the literature But in the first difference, we usually remove the unit root problem. But why we are getting the AIC as of level. I am not clear. How to check for the autocorrelation for the lag ADF is considering?

Regards,
Upananda

The ADF statistic (final column) is the test for the unit root. As you can see, those are most decidedly not the same between your two @ADFAUTOSELECTs. The first set of columns are to help choose the "nuisance" parameter of the number of augmenting lags. They don't tell you anything about the UR test as you can see by comparing the two sets of output that you have.

The point of doing the various IC tests is to pick a lag length which largely removes the residual autocorrelation. The chosen lag (by any criterion) will come reasonably close to doing that. If there was really substantial remaining residual autocorrelation beyond what is handled by a certain number of lags, it would produce a better IC value for a longer lag. If you look at the original test, you'll see that the ADF column is very consistent from lag to lag which makes sense since the first difference is probably fairly close to white noise. The ADF statistics on the first difference aren't quite as stable across lags numerically, but all of those values are way, way out in the tails of the unit root test so in all cases you would emphatically reject that the differenced series had a unit root.

Note, BTW, that if DET=TREND is appropriate for the original series, DET=CONSTANT would be correct for the differenced series.

Dear Sir,

I am grateful to you for your reply. I want to know the following issues:

1. Is there any rule of thumb to choose the optimal lag ( as per walter enders the smallest value of any IC is the significant one) in my case, for the level series, all the IC values are negative. Aic is indifferent as the AIC value is same across all the lag i.e., -8.439 but still it is showing at 3rd lag it is significant. Whereas, BIC, HQ shows significant at lag o ( -8.430 being the smallest value as all the value are negative)

2. Am i supposed to take BIC and HQ for final selection of my lag.

I will take your suggestion to take a call on stationarity test of first difference of the series.

With

upani wrote:Dear Sir,

I am grateful to you for your reply. I want to know the following issues:

1. Is there any rule of thumb to choose the optimal lag ( as per walter enders the smallest value of any IC is the significant one) in my case, for the level series, all the IC values are negative. Aic is indifferent as the AIC value is same across all the lag i.e., -8.439 but still it is showing at 3rd lag it is significant. Whereas, BIC, HQ shows significant at lag o ( -8.430 being the smallest value as all the value are negative)

You pick a criterion and pick the minimizing lag length for that criterion. Again, it doesn't matter as long as the results of the ADF test are qualitatively the same. The fact that the IC values are negative is completely irrelevant---the values of those depend upon the scale of the data. Multiply the data by 100, and you'll get much bigger numbers, but will get exactly the same decision (in fact, exactly the same differences between values). BTW, all these criteria are dominated by -2 x log likelihood, which means that a negative value corresponds to a positive log likelihood (again, not that that matters).

upani wrote: 2. Am i supposed to take BIC and HQ for final selection of my lag.

I will take your suggestion to take a call on stationarity test of first difference of the series.

Since they give the same result, does it matter?