Analyzing and comparing complex environmental time series using a cumulative sums approach

Cumulative sums (Cusums) are a simple, efficient statistical method developed for process control and increasingly used to determine underlying features of time series. Here, two useful applications of Cusums to environmental time series are presented: Cusums in the time domain and plotting Cusum-transformed variables against non-transformed variables to extract meaning in the context of driver-response relationships. These statistical analyses are simple to conduct and provide valuable information about trends, patterns and thresholds of time-series over time and in relation to potential driver variables. In addition, this work investigates the robustness of the Cusum transform to various characteristics of environmental time series that challenge conventional statistical methods. In summary, this work presents: • Cusum methods to derive meaning from complex environmental time series. • Effects of common time series issues on the Cusums method. • Application to real-world datasets.