Intersection–union tests for characterising recent changes in smoothed indicator time series

Using indicator time series for assessment and management requires methods for characterising recent time trends. We propose an approach where first the indicator time series is smoothed using a generalised additive model with optimal selection of the degree of smoothness. Second an intersection–union test is carried out using two test statistics which are the occurrence of the global maximum (or minimum) within the most recent years and the signs of the estimated annual first derivatives of the smoothed indicator times series during the same period, including years with missing data. The proposed test is applied to fish abundance indices for the North Sea, for which it is they are able to pick up changes happening during the last 3–5 years in contrast to linear regression and the Mann–Kendall test which find much fewer significant recent trends. An additional test for changes in trends using the second derivatives of the smoothed indicator time series provide early warnings for subsequent trends for certain species.