Exponential smoothing for time series with outliers

Tomáš Hanzák; Tomáš Cipra

Kybernetika (2011)

  • Volume: 47, Issue: 2, page 165-178
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Hanzák, Tomáš, and Cipra, Tomáš. "Exponential smoothing for time series with outliers." Kybernetika 47.2 (2011): 165-178. <http://eudml.org/doc/197187>.

@article{Hanzák2011,
abstract = {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.},
author = {Hanzák, Tomáš, Cipra, Tomáš},
journal = {Kybernetika},
keywords = {exponential smoothing; Kalman filter; outliers; robust smoothing and forecasting; Kalman filter; outliers; robust smoothing and forecasting},
language = {eng},
number = {2},
pages = {165-178},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exponential smoothing for time series with outliers},
url = {http://eudml.org/doc/197187},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Hanzák, Tomáš
AU - Cipra, Tomáš
TI - Exponential smoothing for time series with outliers
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 2
SP - 165
EP - 178
AB - 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.
LA - eng
KW - exponential smoothing; Kalman filter; outliers; robust smoothing and forecasting; Kalman filter; outliers; robust smoothing and forecasting
UR - http://eudml.org/doc/197187
ER -

References

top
  1. Abraham, B., Ledolter, J., Statistical Methods for Forecasting, Wiley, New York 1983. (1983) Zbl0587.62175MR0719535
  2. Anděl, J., Zichová, J., 10.1081/STA-120015019, Comm. Statist. Theory Methods 31 (2002), 2101–2111. (2002) Zbl1051.62070MR1946313DOI10.1081/STA-120015019
  3. Cipra, T., Some problems of exponential smoothing, Appl. Math. 34 (1989), 161–169. (1989) Zbl0673.62079MR0990303
  4. Cipra, T., 10.1002/for.3980110106, J. Forecasting 11 (1992), 57–69. (1992) DOI10.1002/for.3980110106
  5. Cipra, T., Romera, R., Robust Kalman filter and its applications in time series analysis, Kybernetika 27 (1991), 481–494. (1991) MR1150938
  6. Cipra, T., Trujillo, J., Rubio, A., 10.1287/mnsc.41.1.174, Management Sci. 41 (1995), 174–178. (1995) Zbl0829.90034DOI10.1287/mnsc.41.1.174
  7. Croux, C., Gelper, S., Fried, R., 10.1007/s10492-008-0002-4, Appl. Math. 53 (2008), 163–176. (2008) Zbl1199.91156MR2411122DOI10.1007/s10492-008-0002-4
  8. Gardner, E. S., Exponential smoothing: The state of the art, J. Forecasting 4 (1985), 1–28. (1985) 
  9. Gardner, E. S., 10.1016/j.ijforecast.2006.03.005, Internat. J. Forecasting 22 (2006), 637–666. (2006) DOI10.1016/j.ijforecast.2006.03.005
  10. Gelper, S., Fried, R., Croux, C., Robust forecasting with exponential and Holt-Winters smoothing, J. Forecasting 29 (2010), 285–300. (2010) Zbl1203.62164MR2752114
  11. Taylor, J. W., 10.1002/for.918, J. Forecasting 23 (2004), 385–404. (2004) DOI10.1002/for.918
  12. Yohai, V., Zamar, R., 10.1080/01621459.1988.10478611, J. Amer. Statist. Assoc. 83 (1988), 406–413. (1988) MR0971366DOI10.1080/01621459.1988.10478611

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.