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.
The algorithm we propose can be extended to detect changes in the variance as well as the mean of a process. This kind of changepoint has received relatively little attention; one exception is recent work by Jandhyala, Fotopoulos and Hawkins @cite_10 .
@cite_10
2036835505
Detection of change-points in normal means is a well-studied problem. The parallel problem of detecting changes in variance has had less attention. The form of the generalized likelihood ratio test statistic has long been known, but its null distribution resisted exact analysis. In this paper, we formulate the change-point problem for a sequence of chi-square random variables. We describe a procedure that is exact for the distribution of the likelihood ratio statistic for all even degrees of freedom, and gives upper and lower bounds for odd (and also for non-integer) degrees of freedom. Both the liberal and conservative bounds for X 2 1 degrees of freedom are shown through simulation to be reasonably tight. The important problem of testing for change in the normal variance of individual observations corresponds to the X 2 1 case. The non-null case is also covered, and confidence intervals for the true change point are derived. The mehhodology is illustrated with an application to quality control in a deep level gold mine. Other applications include ambulatory monitoring of medical data and econometrics.