Significance of Patterns in Time Series Collections

Time series are a class of data whose complexity and rich structure make it difficult for data mining tools to extract meaningful patterns from them, and in particular to prune away the false positive patterns. Wavelet-based methods have recently become the preferred way for significance testing of time series and time series collections, but these methods are still often based on fairly ad hoc bootstrapping techniques in the wavelet domain without a disciplined null model analysis. We propose a new well-grounded null model for time series collections that also sets minimum requirements for realistic resampling methods. We compare it to the null models of common resampling methods and introduce a new randomization method that is compatible with the proposed null model. We conduct experiments on real and synthetic datasets to compare the behavior of the various methods and reflect the results to the differences in their null models. Compared with the other methods, our experiments suggest that the proposed method gives fewer Type I and Type II errors across a range of statistics