SiZer for time series: A new approach to the analysis of trends

Abstract

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.