Abstract
In this paper, a new method for detecting multiple structural breaks, i.e. undesired changes of signal behavior, is presented and applied to artificial and real-world data. It will be shown how Chernoff Bounds can be used for high-performance change-point detection after preprocessing arbitrary time series to binary random variables using adequate transformation routines. The algorithm is evaluated on artificial time series and compared to state of the art methods. The developed algorithm is competitive to state of the art methods in terms of classification errors but is considerably faster especially when dealing with long time series. Theoretical results on artificial data from part one of this paper are applied to real-world time series from a pharmaceutical wholesaler and show striking improvement in terms of forecast error reduction, thereby greatly improving forecast quality. In order to test the effect of structural break detection on forecast quality, state of the art forecast algorithms are applied to time series with and without previous application of structural break detection methods.
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References
Perron, P.: Dealing with Structural Breaks. Palgrave handbook of econometrics 1, 278–352 (2006)
Kawahara, Y., Sugiyama, M.: Change-point Detection in Time Series Data by Direct Density-Ratio Estimation. In: Proceedings of 2009 SIAM International Conference on Data Mining (SDM 2009), pp. 389–400 (2009)
Markou, M., Singh, S.: Novelty Detection: a Review–Part 1: Statistical Approaches. Signal Processing 83, 2481–2497 (2003)
Guralnik, V., Srivastava, J.: Event Detection from Time Series Data. In: Proceedings of the 5th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 33–42. ACM (1999)
Ma, J., Perkins, S.: Time Series Novelty Detection Using One-class Support Vector Machines. In: Proceedings of the International Joint Conference on Neural Networks, vol. 3, pp. 1741–1745 (2003)
Ibaida, A., Khalil, I., Sufi, F.: Cardiac abnormalities detection from compressed ECG in wireless telemonitoring using principal components analysis (PCA). In: 2009 5th International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), pp. 207–212. IEEE (2010)
Feller, S., Chevalier, R., Morsili, S.: Parameter Disaggregation for High Dimensional Time Series Data on the Example of a Gas Turbine. In: Proceedings of the 38th ESReDA Seminar, Pécs, H, pp. 13–26 (2010)
Murad, U., Pinkas, G.: Unsupervised Profiling for Identifying Superimposed Fraud. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 251–261. Springer, Heidelberg (1999)
Fujimaki, R., Yairi, T., Machida, K.: An Approach to Spacecraft Anomaly Detection Problem Using Kernel Feature Space. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, pp. 401–410. ACM (2005)
Schwabacher, M., Oza, N., Matthews, B.: Unsupervised Anomaly Detection for Liquid-Fueled Rocket Propulsion Health Monitoring. In: Proceedings of the AIAA Infotech@ Aerospace Conference. American Institute for Aeronautics and Astronautics, Inc., Reston (2007)
Gustafsson, F.: Estimation and Change Detection of Tire-Road Friction Using the Wheel Slip. IEEE Control System Magazine 18, 42–49 (1998)
Ide, T., Kashima, H.: Eigenspace-based Anomaly Detection in Computer Systems. In: Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 440–449. ACM (2004)
Chandola, V., Banerjee, A., Kumar, V.: Anomaly detection: A survey. ACM Computing Surveys (CSUR) 41, 1–58 (2009)
Basseville, M., Nikiforov, I.: Detection of Abrupt Changes: Theory and Application. Prentice-Hall, Inc. (1993)
Chernoff, H.: A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations. The Annals of Mathematical Statistics 23, 493–507 (1952)
Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press (2007)
Hartigan, J., Wong, M.: Algorithm AS 136: A k-means Clustering Algorithm. Journal of the Royal Statistical Society. Series C (Applied Statistics) 28, 100–108 (1979)
Wadsworth, H.: Handbook of statistical methods for engineers and scientists. McGraw-Hill Professional (1997)
Tsay, R.: Analysis of Financial Time Series. Wiley-Interscience (2005)
Strang, G.: Wavelets and dilation equations: A brief introduction. Siam Review 31, 614–627 (1989)
Feller, W.: An introduction to probability theory and its applications. Wiley-India (2009)
Wald, A.: Sequential Tests of Statistical Hypotheses. The Annals of Mathematical Statistics 16, 117–186 (1945)
Herzog, J.: Dynamics Sensor Validation for Reusable Launch Vehicle Propulsion. Presented at 34th AIAA/ASME/ASEE Joint Propulsion Conference and Exhibit, Cleveland, OH, US, July 13-15 (1998)
Taylor, J.: Multi-item sales forecasting with total and split exponential smoothing. Journal of the Operational Research Society (2010)
Gelper, S., Fried, R., Croux, C.: Robust forecasting with exponential and Holt-Winters smoothing. Journal of Forecasting 29, 285–300 (2010)
Holt, C.: Forecasting trends and seasonals by exponentially weighted moving averages. ONR Memorandum 52 (1957)
Brown, R.: Statistical forecasting for inventory control. McGraw-Hill, New York (1959)
Gardner Jr., E.: Exponential smoothing: The state of the art. Journal of Forecasting 4, 1–28 (1985)
Makridakis, S., Wheelwright, S., Hyndman, R.: Forecasting methods and applications. Wiley-India (2008)
Ng, T., Skitmore, M., Wong, K.: Using genetic algorithms and linear regression analysis for private housing demand forecast. Building and Environment 43, 1171–1184 (2008)
Xia, B., Zhao, C.: The Application of Multiple Regression Analysis Forecast in Economical Forecast: The Demand Forecast of Our Country Industry Lavation Machinery in the Year of 2008 and 2009. In: Second International Workshop on Knowledge Discovery and Data Mining, WKDD 2009, pp. 405–408 (2009)
Pinson, P., Nielsen, H., Madsen, H., Nielsen, T.: Local linear regression with adaptive orthogonal fitting for the wind power application. Statistics and Computing 18, 59–71 (2008)
Feller, S., Pauli, D., Kmiecik, F.: Robust AAKR and Modern Signal Transformation Methods for Fault Detection and Analysis. In: Proceedings of the 37th ESReDA Seminar, Baden, CH, pp. 57–63 (2009)
Zeileis, A., Leisch, F., Kleiber, C., Hornik, K.: Monitoring Structural Change in Dynamic Econometric Models. Journal of Applied Econometrics 20, 99–121 (2005)
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Pauli, D., Lorion, Y., Feller, S., Rupp, B., Timm, I.J. (2013). Using Chernoff’s Bounding Method for High-Performance Structural Break Detection and Forecast Error Reduction. In: Ferrier, JL., Bernard, A., Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31353-0_10
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DOI: https://doi.org/10.1007/978-3-642-31353-0_10
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