Generalized M-fluctuation tests for parameter instability

A general class of fluctuation tests for parameter instability in an M-estimation framework is suggested. Tests from this framework can be constructed by first choosing an appropriate estimation technique, deriving a partial sum process of the estimation scores that captures instabilities over time, and aggregating this process to a test statistic by using a suitable scalar functional. Inference for these tests is based on functional central limit theorems, which are derived under the null hypothesis of parameter stability and local alternatives. For (generalized) linear regression models, concrete tests are derived, which cover several known tests for (approximately) normal data but also allow for testing for parameter instability in regressions with binary or count data. The usefulness of the test procedures—complemented by powerful visualizations derived from these—is illustrated using Dow Jones industrial average stock returns, youth homicides in Boston, USA, and illegitimate births in Grossarl, Austria.