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Interpretation of augmented Dickey-Fuller results

  1. Jun 23, 2015 #1

    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.)

    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!



    Attached Files:

    Last edited: Jun 23, 2015
  2. jcsd
  3. Jun 28, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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