Daumer, Martin; Falk, M.; Beyer, U.
On-line monitoring using Multi-Process Kalman Filtering.
Collaborative Research Center 386, Discussion Paper 54
On-line monitoring of time series becomes more and more important in different areas of application like medicine, biometry and finance. In medicine, on-line monitoring of patients after transplantation of renals (Smith83) is an easy and prominent example. In finance, fast end reliable recognition of changes in level and trend of intra-daily stock market prices is of obvious interest for ordering and purchasing. In this project, we currently consider monitoring of surgical data like heart-rate, blood pressure and oxygenation. From a statistical point of view, on-line monitoring can be considered as on-line detection of changepoints in time series. That means, changepoints have to be detected in real time as new observations come in, usually in short time intervals. Retrospective detection of changepoints, after the whole batch of observations has been recorded, is nice but useless in monitoring patients during an operation.
There are various statistical approaches conceivable for on-line detection of changepoints in time series. Dynamic or state space models seem particularly well suited because ``filtering'' has historically been developed exactly for on-line estimation of the ``state'' of some system. Our approach is based on a recent extension of the so-called multi-process Kalman filter for changepoint detection (Schnatter94). It turned out, however, that some important issues for adequate and reliable application have to be considered, in particular the (appropriate) handling of outliers and, as a central point, adaptive on-line estimation of control- or hyper-parameters. In this paper, we describe a filter model that has this features and can be implemented in such a way that it is useful for real time applications with high frequency time series data.
Recently, simulation based methods for estimation of non-Gaussian dynamic models have been proposed that may also be adapted and generalized for the purpose of changepoint detection. Most of them solve the smoothing problem, but very recently some proposals have been made that could be useful also for filtering and, thus, for on-line monitoring (Kitagawa96a,Kitagawa96b,Shephard96). If these approaches are a useful alternative to our development needs a careful comparison in future and is beyond the scope of this paper.