Title:
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Exponential smoothing for time series with outliers (English) |
Author:
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Hanzák, Tomáš |
Author:
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Cipra, Tomáš |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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47 |
Issue:
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2 |
Year:
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2011 |
Pages:
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165-178 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied mainly to various types of exponential smoothing (recursive estimation in Box-Jenkins models with outliers is also mentioned). The methods are demonstrated using simulated data. (English) |
Keyword:
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exponential smoothing |
Keyword:
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Kalman filter |
Keyword:
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outliers |
Keyword:
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robust smoothing and forecasting |
MSC:
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60G35 |
MSC:
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62M10 |
MSC:
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62M20 |
MSC:
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90A20 |
idZBL:
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Zbl 1220.62114 |
idMR:
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MR2828571 |
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Date available:
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2011-06-06T14:51:48Z |
Last updated:
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2013-09-22 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/141565 |
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Reference:
|
[1] Abraham, B., Ledolter, J.: Statistical Methods for Forecasting.Wiley, New York 1983. Zbl 0587.62175, MR 0719535 |
Reference:
|
[2] Anděl, J., Zichová, J.: A method for estimating parameter in nonnegative MA(1) models.Comm. Statist. Theory Methods 31 (2002), 2101–2111. Zbl 1051.62070, MR 1946313, 10.1081/STA-120015019 |
Reference:
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[3] Cipra, T.: Some problems of exponential smoothing.Appl. Math. 34 (1989), 161–169. Zbl 0673.62079, MR 0990303 |
Reference:
|
[4] Cipra, T.: Robust exponential smoothing.J. Forecasting 11 (1992), 57–69. 10.1002/for.3980110106 |
Reference:
|
[5] Cipra, T., Romera, R.: Robust Kalman filter and its applications in time series analysis.Kybernetika 27 (1991), 481–494. MR 1150938 |
Reference:
|
[6] Cipra, T., Trujillo, J., Rubio, A.: Holt-Winters method with missing observations.Management Sci. 41 (1995), 174–178. Zbl 0829.90034, 10.1287/mnsc.41.1.174 |
Reference:
|
[7] Croux, C., Gelper, S., Fried, R.: Computational aspects of robust Holt-Winters smoothing based on M-estimation.Appl. Math. 53 (2008), 163–176. Zbl 1199.91156, MR 2411122, 10.1007/s10492-008-0002-4 |
Reference:
|
[8] Gardner, E. S.: Exponential smoothing: The state of the art.J. Forecasting 4 (1985), 1–28. |
Reference:
|
[9] Gardner, E. S.: Exponential smoothing: The state of the art - Part II.Internat. J. Forecasting 22 (2006), 637–666. 10.1016/j.ijforecast.2006.03.005 |
Reference:
|
[10] Gelper, S., Fried, R., Croux, C.: Robust forecasting with exponential and Holt-Winters smoothing.J. Forecasting 29 (2010), 285–300. Zbl 1203.62164, MR 2752114 |
Reference:
|
[11] Taylor, J. W.: Smooth transition exponential smoothing.J. Forecasting 23 (2004), 385–404. 10.1002/for.918 |
Reference:
|
[12] Yohai, V., Zamar, R.: High break down point estimates of regression by means of the minimization of an efficient scale.J. Amer. Statist. Assoc. 83 (1988), 406–413. MR 0971366, 10.1080/01621459.1988.10478611 |
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