Optimal Prediction of Events in Time Series

Anders Svensson and Jan Holst

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998

ISSN 0281-1944
ISRN LUTFD2/TFMS--3142--SE


Abstract:
This paper presents a technique for constructing explicit event predictors for linear Gaussian time series. The events can be rather general e.g. that a process value is above a certain level or that the process crosses a certain level. The event predictors are optimal, meaning that they have the lowest probability of false alarms for a given probability of detecting the events.
The complexity of the optimal event predictors depends on the process models, how the events are defined and the number of old process values used for predictions.
Simulations for different types of events have been made and the optimal event predictors have been applied to real data series consisting of water levels in the Baltic Sea. The results agree with those from theoretical calculations, although the number of false alarms is rather high due to the difficulties in modelling water levels.
Key words:
Catastrophe, Alarm, Alarm Prediction, Event Prediction, Stochastic Process, ARMA-process, Level-Crossings.