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Empirical calibration of time series monitoring methods using receiver operating characteristic curves

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  • Cohen, Jacqueline
  • Garman, Samuel
  • Gorr, Wilpen
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    Abstract

    Time series monitoring methods, such as the Brown and Trigg methods, have the purpose of detecting pattern breaks (or "signals") in time series data reliably and in a timely fashion. Traditionally, researchers have used the average run length (ARL) statistic on results from generated signal occurrences in simulated time series data to calibrate and evaluate these methods, with a focus on timeliness of signal detection. This paper investigates the receiver operating characteristic (ROC) framework, well-known in the diagnostic decision making literature, as an alternative to ARL analysis for time series monitoring methods. ROC analysis traditionally uses real data to address the inherent tradeoff in signal detection between the true and false positive rates when varying control limits. We illustrate ROC analysis using time series data on crime at the patrol district level in two cities, and use the concept of Pareto frontier ROC curves and reverse functions for methods such as Brown's and Trigg's that have parameters affecting signal-detection performance. We compare the Brown and Trigg methods to three benchmark methods, including one commonly used in practice. The Brown and Trigg methods collapse to the same simple method on the Pareto frontier and dominate the benchmark methods under most conditions. The worst method is the one commonly used in practice.

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    File URL: http://www.sciencedirect.com/science/article/B6V92-4V64YJ0-3/2/658c26f199b61a4a614d188165332506
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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 25 (2009)
    Issue (Month): 3 (July)
    Pages: 484-497

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    Handle: RePEc:eee:intfor:v:25:y:2009:i:3:p:484-497

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    Web page: http://www.elsevier.com/locate/ijforecast

    Related research

    Keywords: Time series monitoring ROC curve Average run length statistic Exponential smoothing Structural breaks Step jumps Outliers;

    References

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    1. Gorr, Wilpen & Olligschlaeger, Andreas & Thompson, Yvonne, 2003. "Short-term forecasting of crime," International Journal of Forecasting, Elsevier, vol. 19(4), pages 579-594.
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    Cited by:
    1. Mathias Drehmann, 2013. "Evaluating early warning indicators of banking crises: Satisfying policy requirements," BIS Working Papers 421, Bank for International Settlements.
    2. Ord, J. Keith & Koehler, Anne B. & Snyder, Ralph D. & Hyndman, Rob J., 2009. "Monitoring processes with changing variances," International Journal of Forecasting, Elsevier, vol. 25(3), pages 518-525, July.
    3. Mathias Drehmann & Kostas Tsatsaronis, 2014. "The credit-to-GDP gap and countercyclical capital buffers: questions and answers," BIS Quarterly Review, Bank for International Settlements, March.
    4. Samohyl, Robert, 2012. "Audits and logistic regression, deciding what really matters in service processes: a case study of a government funding agency for research grants," MPRA Paper 41557, University Library of Munich, Germany.
    5. Gorr, Wilpen L. & Schneider, Matthew J., 2013. "Large-change forecast accuracy: Reanalysis of M3-Competition data using receiver operating characteristic analysis," International Journal of Forecasting, Elsevier, vol. 29(2), pages 274-281.

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