Generalized M-fluctuation tests for parameter instability

A general class of
uctuation 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 which 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 (general-
ized) 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 power-
ful visualizations derived from these|is illustrated using Dow Jones industrial average stock
returns, youth homicides in Boston, USA, and illegitimate births in Großarl, Austria.