Analyses of interventions and structural breaks in marine and fisheries time series: Detection of shifts using iterative methods

Regime shifts in ecosystems whose patterns and properties may be very complex and thus manifold have profound implications for sustainability. Detecting structural breaks in natural processes, however, turns out to be an ambitious task because the lack of well defined target values and reference periods renders application of standard statistical (process or quality) control methods all but impossible. We develop an iterative procedure combining econometric, time series and quantile methods that produce a graphic display referred to as a “shiftogram,” which indicates potential shifts within univariate components of an ecosystem of interest by characterizing their specific and often fairly complex properties. The shiftogram approach can be routinely applied as a scanning device to any (univariate) time series. We provide a search algorithm that iteratively looks for the best value of some quality-of-fit criterion for a time series where the break point is not known beforehand. The approach is demonstrated by the application to univariate examples of fish recruitment, a climate change phenomenon and a canonical variable bundling the effect of different biodiversity indices. Analysis of ecosystem level shifts (i.e. regime shifts) can then be conducted by applying the shiftogram method to multiple component variables and examining correspondence among their resulting shift point and shift types. Alternatively we illustrate how regime shifts can be examined directly by applying the shiftogram approach to multivariate time series data after reduction to a univariate case through canonical data reduction techniques.