Why do I receive unexpected results in the test statistics returned by DFTSTEST in GARCH Toolbox 2.3.1 (R2007a)?

I am performing a Dickey-Fuller univariate unit root test on my data.

When I execute the following:

[H,PValue,Tstat,CV]=dfTSTest(z,2,.05,'t')

I receive the following warning and results:

 Warning: Test statistic #1 invalid: non-stationary polynomial of lagged changes.

 > In dfTSTest at 283

 H =

 0

 PValue =

 NaN

 Tstat =

 NaN

 CV =

 NaN

I understand that the warning specifies that the polynomial coefficients of the lagged differences of time series z are for a non-stationary process. Does this contradict the assumption of a unit root process?

Also, what is the test statistic # 1 exactly and why is the null hypothesis accepted if no test statistics are computed?

Answer 1

[MathWorks Support Team]

The assumption in DFTSTEST of an underlying root process with drift is accepted unless sufficient evidence exists to reject it. In this light, the polynomial issue is seen as invalidating the test, but not explicitly rejecting it.

The warning message is letting you know that the test performed encountered a non-stationary polynomial. As this is the only test performed, the null hypothesis is accepted (H=0), but it just so happens to be the only test performed. The test is therefore not explicitly rejected.

To perform more tests, you could, for instance, perform the same test on the same time series, but at several values for the input lags.