A simple and general change-point identifier.
In a not-necessarily-stationary time-series, a Moving F statistic can identify points of change in the nature of the series model (the estimate of the underlying data-generating process), in its parameters, in residual variability, or in any combination of these. In addition, it can uncover changes masked by a reduction in residual variability. Patterns in the forces giving rise to the data may often be perceived. To form the Moving F, a theory of the process or a regression method on a baseline sample estimates the series model and the residual mean square about it is calculated. This series model is extended past the baseline with residuals assumed to be normally distributed. The Moving F is calculated as the moving average of squared deviations about the series model in ratio to the baseline mean square. The Moving F crossing the critical F identifies a change in the series model, i.e. signals its presence and location. In our experience, this Moving F method is easier to use than other commonly employed change-point identifiers (CUSUM, EWMA, data-based bandwidth selection, MCMC) and has been found to work in several situations where some other identifiers fail. (MCMC is more general, but requires advanced statistical ability.) Examples given are monitored prostate specific antigen in a post-treatment prostate cancer patient and detection of Harold Shipman's medical murders. Moving F is 'simple and general' in the sense of both simultaneously; we have not found another relatively simple method to be as general.