How can Dickey fuller test give -ve value for t-stat?



I have been implementing dickey fuller test after gaining an understanding of its procedure… The relevant equations are

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I have obtained the value for t-stat as +ve and hence when comparing with the table for alpha= 0.05 the result shows it is not stationary. I am confident that my data is stationary because on plotting the data it’s stationary.

What I dont understand is how can the t-stat value ever be negative when numtr and denmtr are positive. The theta value or p_hat is positive(by OLS estimation) and SE as it has squares in the equation will also yield a +ve value.

My assumption:

Can it be because, rooting in SE gives -ve value(as square of a number, both +ve and -ve is the same). Or my theta value has to be -ve but can that be?

Any help on this great thanx.


Try to read this and see if this helps.

And this is a good read to understand how to campare t stat with Tau critical value.

Also a good way to understand why the values are negative. 1 tailed t test stat.