# Understanding results from Augmented Dickey Fuller test

I have no background in statistics/econometrics but some theory I'm applying to geophysics data requires the data to be stationary (or at least trend-stationary) and I don't believe they are.

I've found matlab code to apply the Augmented Dickey-Fuller test (from here - https://ideas.repec.org/c/boc/bocode/t871806.html) on the attached timeseries. (The red trend is a background trend I might use later but for now I want to test the original blue data.)

The results come in the form:

sigma     dw      beta0   beta1

tpp       dh      t0      t1

tppsig    dhsig   NaN     tsig1


The results are:

123.248    2.0302   115.7256    -0.0356

-14.4567  -1.8068    15.3695   -15.5241

0.01     0.0708   NaN          0.01


where sigma = the estimated standard error of the residuals;
dw = the Durbin-Watson statistics of the residuals;
dh = the Durbin h statistic of the residuals;
dhsig = the level of significance at which the (two-sided) null hypothesis of no (first-order) autocorrelation in the residuals is rejected

beta_0, beta_1 = the estimated values of the coefficients (as above)

t_0, t_1 = the (uncorrected) t-ratios on the coefficients;
tpp = the Phillips-Perron corrected t-ratio on beta_1
tsig_1,tppsig = the levels at which t_1 and tpp are statistically significantly, using Dickey-Fuller critical values;

So, reject a unit root if t_1 in the ADF regression is statistically significant, e.g. tsig_1 <= 0.1, AND the residuals are not correlated (otherwise the test statistic is inefficient), OR if tpp (in any regression) is statistically significant (- or both). (Reject random walk, if unit root is rejected, or some dlags are significant, or both.)

MY ATTEMPT AT INTERPRETATION: tpp is less than tpp_sig so the Phillips-Perron corrected t-ration is not significant. So the data could still be stationary.

dh is less than dh_sig. Does this mean that the the data are not correlated? This would be surprising as I know the fluctuations do occur over a typical timescale.

t_1 is less than tsig_1 so the t_ratio is not significant and the timeseries is stationary.

Does that make sense? It doesn't to me! 