Dickey fuller test with time trend

[@davidderosa2985]

Mr. Lambert -- these videos of yours are really a great resource for students learning time series analysis. Great Job!

[@141Gregs]

I really wish I'd seen your videos at the start of my degree. Thanks so much.

[@hadadvitor]

Great timing for me, Ben. Please keep 'em coming! :)

[@UCKszbcV]

Thanks for the video Ben!. If we have a time series (ts) that rejects the null of the ADF test with trend, but fails to reject ADF test with constant, or without constant, can we say that this ts is I(0) and has no unit root?

[@stanislavasimeonova5346]

Just a quick question. Why adding a time trend implies that y_t is quadratic in t? Many thanks

[@yuchaofan]

This is my non-rigorous way of thinking about it. If delta y (think dy/dt) is a linear function of t, then integrating that to get y_t (think y(t)) means that y(t) has to be a function of t^2.

[@chrislam1341]

would you also show explicitly the DF table with time trend please?, as there are several video that you mention about there is a more rigorous DF table, I would like to know what does it actually look like, Thanks.

[@SpartacanUsuals]

Hi, I will add that to my list of things to do. Best, Ben

[@franziskakatharina1486]

How to calculate delta hat? It would save my life if you can explain this please!

[@zenapsgas]

But how do we estimate sigma? How do we find the t-static?

[@hongsheny67]

I understand `-ve` means a negative value, but how does it abbreviates to `ve`?

[@NaBiSc0DiSc0]

fantastic

[@cmfrtblynmb02]

This is the only one I did not understand well in all your videos. Why do we add a time trend to difference? What if I don't want to test a quadratic random walk time series?

[@Thayme]

You can add a time trend to determine if a time series is trend-stationary. If you were to run the version of the DF test Ben wrote in this video and found that the coefficient on time was significant, you would use this model to check if the time series is stationary (ie, use this value of sigma to do the test). Trying to do the test with a different model (ie, one with only a constant alpha), would suffer from omitted variable bias and the value of sigma would be incorrect (sigma would "steal credit" for omitted gamma's work)