  Smoothing methods and SiZer are a useful statistical tool for discovering
statistically significant structure in data. Based on scale space ideas
originally developed in the computer vision literature, SiZer (SIgnificant ZERo
crossing of the derivatives) is a graphical device to assess which observed
features are `really there' and which are just spurious sampling artifacts. In
this paper, we develop SiZer like ideas in time series analysis to address the
important issue of significance of trends. This is not a straightforward
extension, since one data set does not contain the information needed to
distinguish `trend' from `dependence'. A new visualization is proposed, which
shows the statistician the range of trade-offs that are available. Simulation
and real data results illustrate the effectiveness of the method.
