Exponential smoothing for irregular time series

Tomáš Cipra; Tomáš Hanzák

Kybernetika (2008)

  • Volume: 44, Issue: 3, page 385-399
  • ISSN: 0023-5954

Abstract

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The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.

How to cite

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Cipra, Tomáš, and Hanzák, Tomáš. "Exponential smoothing for irregular time series." Kybernetika 44.3 (2008): 385-399. <http://eudml.org/doc/33935>.

@article{Cipra2008,
abstract = {The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.},
author = {Cipra, Tomáš, Hanzák, Tomáš},
journal = {Kybernetika},
keywords = {ARIMA model; exponential smoothing of order $m$; discounted least squares; irregular observations; maximum likelihood; simple exponential smoothing; time series; ARIMA model; exponential smoothing of order ; discounted least squares; irregular observations; maximum likelihood},
language = {eng},
number = {3},
pages = {385-399},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exponential smoothing for irregular time series},
url = {http://eudml.org/doc/33935},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Cipra, Tomáš
AU - Hanzák, Tomáš
TI - Exponential smoothing for irregular time series
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 3
SP - 385
EP - 399
AB - The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.
LA - eng
KW - ARIMA model; exponential smoothing of order $m$; discounted least squares; irregular observations; maximum likelihood; simple exponential smoothing; time series; ARIMA model; exponential smoothing of order ; discounted least squares; irregular observations; maximum likelihood
UR - http://eudml.org/doc/33935
ER -

References

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  1. Abraham B., Ledolter J., Statistical Methods for Forecasting, Wiley, New York 1983 Zbl1082.62079MR0719535
  2. Aldrin M., Damsleth E., Forecasting non-seasonal time series with missing observations, J. Forecasting 8 (1989), 97–116 (1989) 
  3. Anděl J., Zichová J., A method for estimating parameter in nonnegative MA(1) models, Comm. Statist. Theory Methods 31 (2002), 2101–2111 Zbl1051.62070MR1946313
  4. Chatfield C., Time-Series Forecasting, Chapman & Hall/CRC, 2002 
  5. Cipra T., Trujillo, J., Rubio A., Holt–Winters method with missing observations, Manag. Sci. 41 (1995), 174–8 (1995) Zbl0829.90034
  6. Cipra T., Exponential smoothing for irregular data, Appl. Math. 51 (2006), 597–604 Zbl1164.62377MR2291784
  7. Wright D. J., Forecasting data published at irregular time intervals using extension of Holt’s method, Manag. Sci. 32 (1986), 499–510 (1986) 
  8. Zichová J., On a method of estimating parameters in non-negative ARMA models, Kybernetika 32 (1996), 409–424 (1996) Zbl0882.62089MR1420132

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