I understand that Dickey Fuller test is trying to figure out if we can reasonably expect a random walk from the autoregression. If null hypothesis is not rejected, we would then first differentiate it to make it stationary.
But then the first difference model shows Change in Xt is equal to Error at time t. What’s the point of deriving this? This is random noise and have no forecasting abilities–it gives me the same information as Xt=Xt-1+Et, so it seems like first differencing doesn’t do anything useful at all.
Once we get unit root from Dickey Fuller test, we should just stop and say that there is no way to correct the time series.