We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that computes, for each index i, the probability that the last (most recent) change point occurred at i. We evaluate this algorithm by applying it to the change point detection problem and comparing it to the generalized likelihood ratio (GLR) algorithm. We find that our algorithm is as good as GLR, or better, over a wide range of scenarios, and that the advantage increases as the signal-to-noise ratio decreases.
Most recently, Vellekoop and Clark propose a nonlinear filtering approach to the changepoint detection problem (but not estimation or tracking) @cite_0 .
@cite_0
2078450032
A benchmark change detection problem is considered which involves the detection of a change of unknown size at an unknown time. Both unknown quantities are modeled by stochastic variables, which allows the problem to be formulated within a Bayesian framework. It turns out that the resulting nonlinear filtering problem is much harder than the well-known detection problem for known sizes of the change, and in particular that it can no longer be solved in a recursive manner. An approximating recursive filter is therefore proposed, which is designed using differential-geometric methods in a suitably chosen space of unnormalized probability densities. The new nonlinear filter can be interpreted as an adaptive version of the celebrated Shiryayev--Wonham equation for the detection of a priori known changes, combined with a modified Kalman filter structure to generate estimates of the unknown size of the change. This intuitively appealing interpretation of the nonlinear filter and its excellent performance in simulation studies indicates that it may be of practical use in realistic change detection problems.