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Keywords:

  • Multiscale;
  • Non-stationary time series;
  • Testing for stationarity;
  • Time series dependence measures;
  • Time series visualization

Summary.  Traditional visualization of time series data often consists of plotting the time series values against time and ‘connecting the dots’. We propose an alternative, multiscale visualization technique, motivated by the scale–space approach in computer vision. In brief, our method also ‘connects the dots’ but uses a range of pens of varying thicknesses for this. The resulting multiscale map, which is termed the thick pen transform, corresponds to viewing the time series from a range of distances. We formally prove that the thick pen transform is a discriminatory statistic for two Gaussian time series with distinct correlation structures. Further, we show interesting possible applications of the thick pen transform to measuring cross-dependence in multivariate time series, classifying time series and testing for stationarity. In particular, we derive the asymptotic distribution of our test statistic and argue that the test is applicable to both linear and non-linear processes under low moment assumptions. Various other aspects of the methodology, including other possible applications, are also discussed.