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Optimal Prediction Of Catastrophes In Autoregressive Moving‐Average Processes

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  • A. Svensson
  • J. Holst
  • R. Lindquist
  • G. Lindgren

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.

Suggested Citation

  • A. Svensson & J. Holst & R. Lindquist & G. Lindgren, 1996. "Optimal Prediction Of Catastrophes In Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(5), pages 511-531, September.
    • Handle: RePEc:bla:jtsera:v:17:y:1996:i:5:p:511-531
    DOI: 10.1111/j.1467-9892.1996.tb00291.x
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    Cited by:

    1. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    2. Pasquale Cirillo & Jürg Hüsler & Pietro Muliere, 2013. "Alarm Systems and Catastrophes from a Diverse Point of View," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 821-839, December.
    3. Taleb, Nassim Nicholas & Bar-Yam, Yaneer & Cirillo, Pasquale, 2022. "On single point forecasts for fat-tailed variables," International Journal of Forecasting, Elsevier, vol. 38(2), pages 413-422.
    4. Nassim Nicholas Taleb & Yaneer Bar-Yam & Pasquale Cirillo, 2020. "On Single Point Forecasts for Fat-Tailed Variables," Papers 2007.16096, arXiv.org.
    5. M. Antunes & M. A. Amaral Turkman & K. F. Turkman, 2003. "A Bayesian Approach to Event Prediction," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 631-646, November.
    6. Halfdan Grage & Jan Holst & Georg Lindgren & Mietek Saklak, 2010. "Level Crossing Prediction with Neural Networks," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 623-645, December.

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