Knicktests

Knicktests are a class of statistical procedures designed to detect localized, abrupt changes in data sequences, referred to as knicks. The tests are suitable for time series, spatial sequences, and functional observations, and can be implemented in parametric or nonparametric forms. They aim to identify short-lived deviations from an assumed baseline or stable process while remaining robust to longer-term trends.

The approach proceeds by sliding a fixed-length window along the data and computing a local deviation statistic at each position. The global knick statistic is the maximum (or sum) of these local values. Under the null hypothesis of no knick, the distribution of the global statistic is approximated via permutation, bootstrap, or asymptotic theory, enabling p-values. Multiple testing is controlled with max-statistic adjustments or cluster-based corrections. Choices include window length, weighting kernel, and one- or two-sided tests.

Variants include Knick-Scan, using smooth sliding windows, and Knick-Cluster, which groups neighboring windows into knick regions. Potential applications span finance (transient price moves), engineering (short faults in manufacturing), neuroscience (burst neural activity), climate science (brief anomalies), and environmental monitoring.

Limitations include sensitivity to window selection, data dependence, computational cost, and interpretation when knicks overlap. The Knicktest framework emerged in methodological studies in the late 2010s, introducing scan- and cluster-based forms for localized change detection.