The point at which a time series changes direction. Determining the true turning point of a time series can be difficult. Despite their popular appeal to practitioners, turning-point measures have limited value because they do not contain information about the magnitude of changes. Furthermore, in most cases, the number of turning points is so small as to lack <a href="search.pl?p=reliability">reliability</a> as a measure of the comparative accuracy of forecasting methods. <o:p></o:p></P>