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Optimal prediction of catastrophes in autoregressive moving-average processes

Svensson, Anders; Holst, Jan LU ; Lindquist, R. and Lindgren, Georg LU (1996) In Journal of Time Series Analysis 17(5). p.511-531
Abstract
Abstract. This paper presents an optimal predictor of level crossings, catastrophes, for autoregressive moving-average processes, and investigates the performance of the predictor. The optimal catastrophe predictor is the predictor that gives a minimal number of false alarms for a fixed detection probability. As a tool for evaluating, comparing and constructing the predictors a method using operating characteristics, i.e. the probability of correct alarm and the probability of detecting a catastrophe for the predictor, is used. An explicit condition for the optimal catastrophe predictor based on linear prediction of future process values is given and compared with a naive catastrophe predictor, which alarms when the predicted process... (More)
Abstract. This paper presents an optimal predictor of level crossings, catastrophes, for autoregressive moving-average processes, and investigates the performance of the predictor. The optimal catastrophe predictor is the predictor that gives a minimal number of false alarms for a fixed detection probability. As a tool for evaluating, comparing and constructing the predictors a method using operating characteristics, i.e. the probability of correct alarm and the probability of detecting a catastrophe for the predictor, is used. An explicit condition for the optimal catastrophe predictor based on linear prediction of future process values is given and compared with a naive catastrophe predictor, which alarms when the predicted process values exceed a given level, and with some different approximations of the optimal predictor. Simulations of the different algorithms are presented, and the performance is shown to agree with the theoretical results. All results indicate that the optimal catastrophe predictor is far better than the naive predictor. They also show that it is possible to construct an approximate catastrophe predictor requiring fewer computations without losing too much of the optimal predictor performance. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Time Series Analysis
volume
17
issue
5
pages
511 - 531
publisher
Wiley-Blackwell
external identifiers
  • scopus:0345980049
ISSN
0143-9782
DOI
10.1111/j.1467-9892.1996.tb00291.x
language
English
LU publication?
yes
id
50c0d6d9-cdb1-4148-94ea-3d91293c6892 (old id 1210457)
date added to LUP
2008-08-14 14:08:34
date last changed
2017-03-15 13:26:57
@article{50c0d6d9-cdb1-4148-94ea-3d91293c6892,
  abstract     = {Abstract. This paper presents an optimal predictor of level crossings, catastrophes, for autoregressive moving-average processes, and investigates the performance of the predictor. The optimal catastrophe predictor is the predictor that gives a minimal number of false alarms for a fixed detection probability. As a tool for evaluating, comparing and constructing the predictors a method using operating characteristics, i.e. the probability of correct alarm and the probability of detecting a catastrophe for the predictor, is used. An explicit condition for the optimal catastrophe predictor based on linear prediction of future process values is given and compared with a naive catastrophe predictor, which alarms when the predicted process values exceed a given level, and with some different approximations of the optimal predictor. Simulations of the different algorithms are presented, and the performance is shown to agree with the theoretical results. All results indicate that the optimal catastrophe predictor is far better than the naive predictor. They also show that it is possible to construct an approximate catastrophe predictor requiring fewer computations without losing too much of the optimal predictor performance.},
  author       = {Svensson, Anders and Holst, Jan and Lindquist, R. and Lindgren, Georg},
  issn         = {0143-9782},
  language     = {eng},
  number       = {5},
  pages        = {511--531},
  publisher    = {Wiley-Blackwell},
  series       = {Journal of Time Series Analysis},
  title        = {Optimal prediction of catastrophes in autoregressive moving-average processes},
  url          = {http://dx.doi.org/10.1111/j.1467-9892.1996.tb00291.x},
  volume       = {17},
  year         = {1996},
}