Detrended line still has a trend I have a line and I have detrended it but it seems to still have a trend. Visually it has one (see jpg) and it has a unit root (Dickey-Fuller) and fails the Durbin-Watson test, so it is not stationary.
The line that I am calling 'detrended' is a plot of the residuals (errors) of a regression of the data on time.
My question is why would a supposedly detrended line still have a trend?

 A: It would still have a trend if you have not properly detrended it.  Trends are a complicated thing, and you may want to re-visit the model you are using to describe the trend.
First of all, if you're using a linear model, it is almost certainly wrong.  You can clearly see a unit root, where the shock in September '06 propagates through time.  The series does not revert to the mean.  I would say this series is begging for a first-order differencing.  That might give you a stationary series you can use for more traditional regression analysis.  If that simple fix doesn't work, try an ARIMA model.  If you don't know what that is, ask!
If I may ask, what is the goal of this analysis?  Could you provide some example data that we might use to help you find a proper model?
A: At a more basic level aren't you assuming that the original graph has two parts that have the same slope but different intercepts, so if you throw a linear regression through it, the regression line should share that slope and split the difference in intercepts?
This isn't true. Try using the points
x=(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) and
y=(1, 2, 3, 4, 5, 16, 17, 18, 19, 20).

The two halves share the same slope (i.e. 1), but a regression through them will not share that slope (it has slope 2.515). The residuals will have a slope (trend) that is the difference between their actual slopes (which may not be the same for each half of your data) and the linear regression's slope.
