Curious unit root p-values = EXACTLY zero.

[Sam Helen]

Dear Stata - community:

Below is a curious result from my unit root tests (Phillips-Perron) with 6 lags and without a trend. I have 3066 cross-sectional units that I am testing on a weekly dataset spanning 3 years.

My question to you is: Why are there so many p-values that are EXACTLY equal to zero, and exactly equal to 1?

Is this evidence of an interesting data feature that I am missing? How could we investigate this further?

As usual your thoughts are extremely appreciated.

Sam

[Nick Cox]

When Stata reports a P-value as say 0.0000 it means <0.00005. Usually there are ways of getting more detail.

Here is a trivial example of different kind. chitesti is from tab_chi on SSC. The very small value doesn't mean anything extraordinary, just indicating a strong rebuttal of the null.

. chitesti 15 0 0 \ 5 5 5

observed frequencies from keyboard; expected frequencies from keyboard

         Pearson chi2(2) =  30.0000   Pr =  0.000
likelihood-ratio chi2(2) =  32.9584   Pr =  0.000

  +-------------------------------------------+
  | observed   expected   obs - exp   Pearson |
  |-------------------------------------------|
  |       15      5.000      10.000     4.472 |
  |        0      5.000      -5.000    -2.236 |
  |        0      5.000      -5.000    -2.236 |
  +-------------------------------------------+

. ret li

scalars:
                  r(k) =  3
                 r(df) =  2
               r(chi2) =  30.00000000000001
                  r(p) =  3.05902320502e-07
            r(chi2_lr) =  32.95836866004329
               r(p_lr) =  6.96917193763e-08
              r(emean) =  5

[Sam Helen]

Nick Cox - you make a lot of sense, and I thank you: It was suggested to me that lots of tiny p-values suggest something conspicuous (a weak test, or possibly >1 unit root). Does any of this ring a bell for you?

[Nick Cox]

I can't comment on unit root tests, but tiny P-values can mean anything between a wonderful discovery and a silly question. I'd show your Stata results to get comments from people who know more about time series tests.

[Sam Helen]

Fair enough! Thank you.