I don't know about time series data, but if the "errors" are independent
(and preferably constant variance), wouldn't this amounts to estimating
zeroes in the first derivative of the trend?  I believe several packages for
smoothing (e.g., KernSmooth and locfit) can estimate derivatives.  J. S.
Marron's SiZer actually tests for significance of the zeroes, but that has
not been implemented in R, AFAIK.  Marron's web site has Matlab code for it.

Andy

> From: Joerg Schaber
> 
> Hi,
> 
> does anybody know of a nice test to detect trend turning 
> points in time 
> series? Possibly with reference?
> Thanks,
> 
> joerg
> 
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