A Brief Overview of the Regime Shift Detection Methods

The methods reviewed here are primarily those that are used in atmospheric and oce-anic (physical and biological) studies. These methods are divided into four groups, depending on the type of shifts they are designed to detect, and placed in Tables 1-4. The tables are self-explanatory and provide a brief description of each method, along with the basic references , as well as their strong and weak points. Shifts in the mean are the most common type of shifts considered in the literature, and as a result, Table 1 is the most populated. The definition of climatic regime shifts, for example , is often based on " differing average climatic levels over a multi-annual duration " (Overland et al., 2005). It is not surprising, therefore, that a major part of the research effort is directed at developing the methods for detecting shifts in the mean. Several approaches can be distinguished: 1. Parametric methods, such as the classical t-test. The methods require an assumption about the probability distribution of the data; 2. Non-parametric methods, such as the Mann–Whitney U-test, Wilcoxon rank sum, or Mann-Kendall test. No assumption about the probability distribution is required; 3. Curve-fitting methods; 4. Bayesian analysis and its variations, such as the Markov chain Monte Carlo method; 5. Regression-based methods; 6. Cumulative sum (CUSUM) methods; and 7. Sequential methods. There are much fewer methods capable of detecting regime shifts in the second-order statistics, such as the variance and power spectrum (Tables 2 and 3). A separate group of methods includes those multivariate methods that are designed to detect shifts in the entire structure of a complex system (Table 4). This is a fast-growing group of methods, and Table 4 will likely require an update soon.