dfuller appears to use incorrect critical values with option "drift"

[James Brugler]

Hello all,

When running Augmented Dickey Fuller tests using the "dfuller" command, Stata reports standard t-distribution critical values when the option "drift" is used, rather than the Interpolated Dickey Fuller critical values. When running the ADF test with either option "trend" or the default, the correct Interpolated Dickey Fuller values are reported.

Code to replicate this is below:

"""
clear all
use http://www.stata-press.com/data/r13/air2

dfuller air, lags(3) trend

dfuller air, lags(3) drift

"""

Using the first test (with trend) I obtain critical values of -4.027, -3.445, -3.145 at the 1%, 5% and 10% levels respectively, which correspond to the correct DF values.

Using the second test (with drift), I obtain critical values of -2.354, -1.656 and -1.288 at the 1%, 5% and 10% levels respectively, which do not correspond to the correct DF values, but instead are the critical values from the t-distribution with 140 observations.

The t-distribution critical values are obviously not valid for the Dickey Fuller test and this appears to be a error in the "dfuller" code.

I am running Stata 15.1 and have recently updated the system.

Any advice on why this is occurring, or confirmation that this is indeed a bug with the "dfuller" command would be highly appreciated.

Thanks,
James

[Sebastian Kripfganz]

That is not a mistake. For the case implied by the drift option, the conventional distributions are applicable. The Stata manual on the dfuller commands states:

Except in the third case, the t-statistic used to test \(H_0: \beta = 0\) does not have a standard distribution.

See also: Hamilton (1994): Time Series Analysis, chapter 17, pages 495-497.

[James Brugler]

Thank you very much for your response. I did not read the help file closely enough to realise that the option "drift" only refers to a change in null hypothesis and not to a change in the regression model from the default. My (incorrect) assumption was that I was specifying that the regression model include a constant by using the drift option, as is the case with some other software (Matlab, Python statsmodel.tsa).

One reason why this was confusing is that the description for the "drift" option at the beginning of the help file reads "include drift term in regression" which can arguably be read to imply that this does change the regression model from the default option to include a constant term, rather than a change in null hypothesis only. As you state, the detailed help file makes it clear that the default does include the constant term, as does the helpfile description for "noconstant".