Impact of Starting Outlier Removal on Accuracy of Time Series Forecasting

Romanuke, Vadim

doi:10.2478/sjpna-2022-0001

Abstract

The presence of an outlier at the starting point of a univariate time series negatively influences the forecasting accuracy. The starting outlier is effectively removed only by making it equal to the second time point value. The forecasting accuracy is significantly improved after the removal. The favorable impact of the starting outlier removal on the time series forecasting accuracy is strong. It is the least favorable for time series with exponential rising. In the worst case of a time series, on average only 7 % to 11 % forecasts after the starting outlier removal are worse than they would be without the removal.

References

[1] Astola J, Kuosmanen P., Fundamentals of Nonlinear Digital Filtering, CRC Press, 1997.
Search in Google Scholar Back to article
[2] Box G., Jenkins G., Time Series Analysis: Forecasting and Control, Holden-day, San Francisco, 1970.
Search in Google Scholar Back to article
[3] Cleveland W. S., Devlin S. J., Locally-weighted regression: an approach to regression analysis by local fitting, ‘Journal of the American Statistical Association’, 1988, Vol. 83, Iss. 403, pp. 596 — 610.10.1080/01621459.1988.10478639
Search in Google Scholar Back to article
[4] Cleveland W. S., Robust locally weighted regression and smoothing scatterplots, ‘Journal of the American Statistical Association’, 1979, Vol. 74, Iss. 368, pp. 829 — 836.10.1080/01621459.1979.10481038
Search in Google Scholar Back to article
[5] Davies L, Gather U., The identification of multiple outliers, ‘Journal of the American Statistical Association’, 1993, Vol. 88, Iss. 423, 782 — 792.10.1080/01621459.1993.10476339
Search in Google Scholar Back to article
[6] Edwards R. E., Functional Analysis. Theory and Applications, Hold, Rinehart and Winston, 1965.
Search in Google Scholar Back to article
[7] Fox J., Weisberg S., An R Companion to Applied Regression (3rd ed.), SAGE, 2018.
Search in Google Scholar Back to article
[8] Gubner J., Probability and Random Processes for Electrical and Computer Engineers, Cam-bridge University Press, 2006.10.1017/CBO9780511813610
Search in Google Scholar Back to article
[9] Hamilton J. D., Time Series Analysis, Princeton University Press, Princeton, NJ, 1994.
Search in Google Scholar Back to article
[10] Han J., Kamber M., Pei J., 12. Outlier detection, in: Data Mining: Concepts and Techniques (Third Edition), Morgan Kaufmann, 2012, pp. 543 — 584.10.1016/B978-0-12-381479-1.00012-5
Search in Google Scholar Back to article
[11] Hyndman R., Koehler A., Another look at measures of forecast accuracy, ‘International Jour-nal of Forecasting’, 2006, Vol. 22, Iss. 4, pp. 679 — 688.10.1016/j.ijforecast.2006.03.001
Search in Google Scholar Back to article
[12] Kotu V., DeshpandeB., Data Science (Second Edition), MorganKaufmann, 2019.
Search in Google Scholar Back to article
[13] Mills T. C., Chapter 8. Unobserved Component Models, Signal Extraction, and Filters, in:Applied Time Series Analysis: A Practical Guide to Modeling and Forecasting, Academic Press, 2019, pp. 131—144.10.1016/B978-0-12-813117-6.00008-9
Search in Google Scholar Back to article
[14] Pankratz A., Forecasting with Univariate Box—Jenkins Models:Concepts and Cases, JohnWiley& Sons, 1983.10.1002/9780470316566
Search in Google Scholar Back to article
[15] Papoulis A., Probability, Random variables and Stochastic processes, McGraw-Hill, 1991.
Search in Google Scholar Back to article
[16] Randel W. J., Filtering and Data Preprocessing for Time Series Analysis, ‘Methods in Experimental Physics’, 1994, Vol. 28, pp. 283—311.10.1016/S0076-695X(08)60260-4
Search in Google Scholar Back to article
[17] Romanuke V.V., Theoretic-game methods of identification of models for multistage technical control and run-in under multivariate uncertainties, Mathematical Modeling andComputational Methods, Vinnytsia National Technical University, Vinnytsia, Ukraine, 2014.
Search in Google Scholar Back to article
[18] Romanuke V.V., Identification of the machining tool wear model via minimax combining and weighting subsequently specific models,‘Information processing systems’, 2015, Iss.12 (137), pp. 106—111.
Search in Google Scholar Back to article
[19] Romanuke V. V., Meta-minimax approach for optimal alternatives subset regarding the change of the risk matrix in ensuring industrial and manufacturing labor safety,‘Herald ofKhmelnytskyi national university. Technicalsciences’, 2015, No.6,pp. 97—99.
Search in Google Scholar Back to article
[20] RomanukeV. V., Appropriateness of DropOut layers and allocation of their 0.5 rates across convolutional neural networks for CIFAR-10, EEACL26, and NORB datasets,‘Applied Computer Systems’, 2017, Vol. 22, pp. 54—63.10.1515/acss-2017-0018
Search in Google Scholar Back to article
[21] Romanuke V. V., An attempt of finding an appropriate number of convolutional layers in CNNs based on benchmarks of heterogeneous datasets,‘Electrical, Control and Communication Engineering’, 2018, Vol. 14, No. 1,pp. 51—57.10.2478/ecce-2018-0006
Search in Google Scholar Back to article
[22] Romanuke V. V., Decision making criteria hybridization for finding optimal decisions’subset regarding changes of the decision function,‘Journal of Uncertain Systems’, 2018, Vol. 12, No.4, pp. 279—291.
Search in Google Scholar Back to article
[23] Romanuke V. V., Minimal total weighted tardiness in tight-tardy single machine preemptive idling-free scheduling,‘Applied ComputerSystems’,2019, Vol. 24, No.2, pp. 150—160.10.2478/acss-2019-0019
Search in Google Scholar Back to article
[24] Romanuke V.V., A minimax approach to mapping partial interval uncertainties into point estimates, ‘Journal of Mathematics and Applications’, 2019, Vol. 42, pp. 147—185.10.7862/rf.2019.10
Search in Google Scholar Back to article
[25] Romanuke V. V., Wind speed distribution directapproximationbyaccumulative statisticsof measurements and root-mean-square deviation control,‘Electrical, Control and Communica-tion Engineering’, 2020, Vol. 16, No. 2, pp. 65—71.10.2478/ecce-2020-0010
Search in Google Scholar Back to article
[26] Savitzky A., Golay M. J. E., Smoothing and differentiation of data by simplified least squares procedures, ‘Analytical Chemistry’, 1964, Vol. 36, Iss. 8, pp. 1627—1639.10.1021/ac60214a047
Search in Google Scholar Back to article
[27] Schelter B., Winterhalder M., Timmer J., Handbook of Time Series Analysis:Recent Theoretical Developments and Applications, Wiley,2006.10.1002/9783527609970
Search in Google Scholar Back to article
[28] Zhao Y., Chapter 7. Outlier detection, in:Rand DataMining:Examples and Case Studies, Academic Press, 2013, pp. 63—73.10.1016/B978-0-12-396963-7.00007-6
Search in Google Scholar Back to article

Impact of Starting Outlier Removal on Accuracy of Time Series Forecasting

Abstract

Paradigm

My account