Optimal Prediction of Events in Time Series
Anders Svensson and Jan Holst
Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998
ISSN 02811944
ISRN LUTFD2/TFMS3142SE

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,
ARMAprocess, LevelCrossings.