Interpretation of augmented Dickey-Fuller results

[BOYLANATOR]

Hi,

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!

Thanks,

BOYLANATOR

 

[mmwave]

Hi BOYLANATOR,

Thank you for sharing your results and concerns. Based on the information provided, it seems like your data may still be stationary. The tpp value being less than tppsig indicates that the Phillips-Perron corrected t-ratio is not significant, which suggests that there is no evidence of a unit root. Additionally, the t_1 value being less than tsig_1 suggests that the t-ratio is not significant and the data is stationary.

However, it is important to note that the results of the Augmented Dickey-Fuller test should not be the only factor in determining whether your data is stationary. It is also important to consider the underlying theory and potential sources of non-stationarity in your data. If you have concerns about the validity of your results, it may be helpful to consult with a statistician or econometrician who can provide a more thorough analysis and interpretation of your data.

Overall, it seems like your interpretation is in line with the results, but it is important to consider other factors and seek additional guidance if needed. I hope this helps and good luck with your analysis.