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I am confused of why my Dickey-Fuller test is significant (which implies stationarity), while the time series clearly exhibits a deterministic trend?

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    $\begingroup$ A deterministic trend does not seem that clear to me. A linear trend --which is the kind of trend considered in the regression model of the Dickey-Fuller test-- is not observed as an overall long-term pattern. The local-level model can be helpful to analyse your data. For software implementing this model you may see these papers. For an illustration you may also see for example this application to temperature trends. $\endgroup$
    – javlacalle
    Commented Dec 22, 2014 at 20:37

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Since you have put the tag "augmented-dickey-fuller", I will assume you did the ADF test with a trend.

So in that case, if you think your series do have a deterministic trend, then the result of the test is indeed correct, because it is trend stationary. That is, once you account for the deterministic trend (as you do in the ADF test), the process is stationary.

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