Tests for anomalous years in the CCAMLR index series (draft)

The properties of a method for detecting anomalous years in CCAMLR index series are discussed. In simple cases this method involves comparing a standardized residual with a critical value obtained on the assumption that the series being considered consists of random values from a constant normal distribution. This idea is extended to situations (a) where the series values are still normally distributed, but contain a linear trend and autocorrelation, and (b) where the series values are from some other constant distribution. For cases like (a) # is proposed that the standardized deviations from a fitted linear regression line are compared with a critical value that is obtained on the assumption that there is no autocorrelation. This test is shown to have good properties even when autocorrelation is present, at least according to one model For cases like (b) it is proposed that a Box-Cox transformation to normality is applied before testing standardized residuals. This test has good properties for data from a wide range of distributions. Some examples are given to illustrate the performance of the proposed methods under various conditions.