This paper introduces a methodology for the identification and characterization of pattern change in large data sets. The procedure includes three methodological components applied in conjunction: (i) the evaluation of scale-symmetry and pattern persistence based on detrended fluctuation analysis and Haar wavelet analysis; we introduce a new way of expressing scale-range-dependent properties using iso-persistence maps; (ii) the evaluation of distributions using L-moments; (iii) the construction and analysis of state phase transition matrices. The latter represents an original methodology applied to time series seen as the expression of dynamic systems evolving from one state to another. Transition matrices are generated for a range of resolution values, and scaling properties of the resulting set of matrices are identified. Moreover, we show that the construction and multi-scale analysis of variable resolution matrices is mathematically equivalent to the determination of the box-dimension for the matrix with the highest resolution, which leads to a significant drop in processing time. We show that the distinct methods applied together are capable of identifying properties of natural time series, which cannot be detected with any of the methods used in separation. The methodological approach introduced here is applied to the monitoring of real natural time series for the detection and characterization of patterns and pattern change; application examples illustrate the broad range of data that can be approached in this way, such as seismicity data, air temperature records, and river discharge records.
