Event Prediction and Bootstrap in Time Series
(1998) Abstract
 Alarm systems are used in many situations, and should be as efficient as possible. In this thesis optimal predictive alarm systems, event predictors, are presented for general linear time series models with external signals. This family of process models include e.g. AR, ARMA, ARMAX and BoxJenkinstype models. An optimal alarm system is characterized by having the least number of false alarms, for a specified probability of detecting the events, the catastrophes. The family of events treated is based on the time series and very general.
When the process parameters are known and the noise distribution is Gaussian, the resulting optimal event predictor is based on predictions of future process values, and the alarm... (More)  Alarm systems are used in many situations, and should be as efficient as possible. In this thesis optimal predictive alarm systems, event predictors, are presented for general linear time series models with external signals. This family of process models include e.g. AR, ARMA, ARMAX and BoxJenkinstype models. An optimal alarm system is characterized by having the least number of false alarms, for a specified probability of detecting the events, the catastrophes. The family of events treated is based on the time series and very general.
When the process parameters are known and the noise distribution is Gaussian, the resulting optimal event predictor is based on predictions of future process values, and the alarm regions can be calculated in advance. Thus the event predictor can be used also in processes with a high sampling rate. It is also possible to construct an event predictor where a major part of the calculations can be made in realtime, which may be of advantage if the process parameters change. The peformance of the event predictors is examined using simulated as well as real data, and they are compared to simpler and more conventional alarm systems.
When the noise distribution is unknown or the process parameters are unknown or timevarying, it is not possible to use the explicit event predictor above. However, statistical bootstrap techniques for calculating the distribution of the future process values can be applied to the problem. The presented bootstrap based event predictor demands large amounts of calculations for AR processes and even more so for ARX processes, but it is much more flexible than the event predictor discussed above, and the performance of the event predictors are comparable. Simulations are used to assess the performance.
The bootstrap technique for ARX processes is also possible to apply to control problems, resulting in a new predictive control algorithm, the bootstrap control, which takes care of arbitrary loss functions and unknown noise distributions, even for small estimation sets. The bootstrap control algorithm has been tested through simulations and was found to work well for complicated loss functions and also for processes with slowly timevarying parameters. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/39056
 author
 Svensson, Anders ^{LU}
 opponent

 Tjöstheim, Dag, Prof., Dept. of Mathematics, Univ. of Bergen, Norway
 organization
 publishing date
 1998
 type
 Thesis
 publication status
 published
 subject
 keywords
 Statistics, bootstrap control., statistical bootstrap, catastrophe, levelcrossings, ARMAX process, Optimal alarm system, time series, optimal event predictor, operations research, programming, actuarial mathematics, Statistik, operationsanalys, programmering, aktuariematematik
 pages
 150 pages
 publisher
 Department of Mathematical Statistics, Lund University
 defense location
 Room C, Math Building
 defense date
 19981120 10:15
 external identifiers

 Other:ISRN: LUTFD2/TFMS1011SE
 ISBN
 9162831658
 language
 English
 LU publication?
 yes
 id
 f950066ef8034933b8ae523d7d522322 (old id 39056)
 date added to LUP
 20070927 16:14:50
 date last changed
 20160919 08:45:01
@phdthesis{f950066ef8034933b8ae523d7d522322, abstract = {Alarm systems are used in many situations, and should be as efficient as possible. In this thesis optimal predictive alarm systems, event predictors, are presented for general linear time series models with external signals. This family of process models include e.g. AR, ARMA, ARMAX and BoxJenkinstype models. An optimal alarm system is characterized by having the least number of false alarms, for a specified probability of detecting the events, the catastrophes. The family of events treated is based on the time series and very general.<br/><br> <br/><br> When the process parameters are known and the noise distribution is Gaussian, the resulting optimal event predictor is based on predictions of future process values, and the alarm regions can be calculated in advance. Thus the event predictor can be used also in processes with a high sampling rate. It is also possible to construct an event predictor where a major part of the calculations can be made in realtime, which may be of advantage if the process parameters change. The peformance of the event predictors is examined using simulated as well as real data, and they are compared to simpler and more conventional alarm systems.<br/><br> <br/><br> When the noise distribution is unknown or the process parameters are unknown or timevarying, it is not possible to use the explicit event predictor above. However, statistical bootstrap techniques for calculating the distribution of the future process values can be applied to the problem. The presented bootstrap based event predictor demands large amounts of calculations for AR processes and even more so for ARX processes, but it is much more flexible than the event predictor discussed above, and the performance of the event predictors are comparable. Simulations are used to assess the performance.<br/><br> <br/><br> The bootstrap technique for ARX processes is also possible to apply to control problems, resulting in a new predictive control algorithm, the bootstrap control, which takes care of arbitrary loss functions and unknown noise distributions, even for small estimation sets. The bootstrap control algorithm has been tested through simulations and was found to work well for complicated loss functions and also for processes with slowly timevarying parameters.}, author = {Svensson, Anders}, isbn = {9162831658}, keyword = {Statistics,bootstrap control.,statistical bootstrap,catastrophe,levelcrossings,ARMAX process,Optimal alarm system,time series,optimal event predictor,operations research,programming,actuarial mathematics,Statistik,operationsanalys,programmering,aktuariematematik}, language = {eng}, pages = {150}, publisher = {Department of Mathematical Statistics, Lund University}, school = {Lund University}, title = {Event Prediction and Bootstrap in Time Series}, year = {1998}, }