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Suppose that dependent variable is a share of sth (for example it is a % of positive answers to the same question in each period of time t). If data shows the unit root problem, what does it mean? Process seems to be non-stationary in levels but stationary in first differences.

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    $\begingroup$ The question "what does it mean" is so general it ends up being unanswerable. Please make your question more specific. $\endgroup$ – Alecos Papadopoulos Oct 16 '14 at 10:30
  • $\begingroup$ Should I use level or first difference time series for building a model? $\endgroup$ – BiXiC Oct 16 '14 at 11:01
  • $\begingroup$ If you don't know your way around non-stationary frameworks, it would be safer to use the first differences. This is the best I can offer for such limited knowledge of your case. $\endgroup$ – Alecos Papadopoulos Oct 16 '14 at 11:08
  • $\begingroup$ My dependent variable is Brand awareness. This is % of people which tells that they know brand name. Obviously it correlate with lagged dependent variables... $\endgroup$ – BiXiC Oct 16 '14 at 12:42
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It can't be non-stationary in unit-root sense. Your variable is limited between 0 and 1. If yo have unit root or a trend, then it should blow up these limits, eventually. So, typical unit root measures such as difference will not work. You have to think up something else.

One example is to apply logit transformation to the dependent variable, then see if the new variable is stationary, and deal with it.

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Have a look at this paper by Giuseppe Cavaliere.

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