Seasonal time series with missing observations

Tomáš Ratinger

Applications of Mathematics (1996)

  • Volume: 41, Issue: 1, page 41-55
  • ISSN: 0862-7940

Abstract

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Popular exponential smoothing methods dealt originally only with equally spaced observations. When time series contains gaps, smoothing constants have to be adjusted. Cipra et al., following Wright’s approach of irregularly spaced observations, have suggested ad hoc modification of smoothing constants for the Holt-Winters smoothing method. In this article the fact that the underlying model of the Holt-Winters method is a certain seasonal ARIMA is used. Minimum mean square error smoothing constants are derived and compared with those of Cipra.

How to cite

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Ratinger, Tomáš. "Seasonal time series with missing observations." Applications of Mathematics 41.1 (1996): 41-55. <http://eudml.org/doc/32936>.

@article{Ratinger1996,
abstract = {Popular exponential smoothing methods dealt originally only with equally spaced observations. When time series contains gaps, smoothing constants have to be adjusted. Cipra et al., following Wright’s approach of irregularly spaced observations, have suggested ad hoc modification of smoothing constants for the Holt-Winters smoothing method. In this article the fact that the underlying model of the Holt-Winters method is a certain seasonal ARIMA is used. Minimum mean square error smoothing constants are derived and compared with those of Cipra.},
author = {Ratinger, Tomáš},
journal = {Applications of Mathematics},
keywords = {Holt-Winters method; missing observations; seasonal ARIMA model; missing observations; seasonal ARIMA model; Holt-Winters method},
language = {eng},
number = {1},
pages = {41-55},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Seasonal time series with missing observations},
url = {http://eudml.org/doc/32936},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Ratinger, Tomáš
TI - Seasonal time series with missing observations
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 1
SP - 41
EP - 55
AB - Popular exponential smoothing methods dealt originally only with equally spaced observations. When time series contains gaps, smoothing constants have to be adjusted. Cipra et al., following Wright’s approach of irregularly spaced observations, have suggested ad hoc modification of smoothing constants for the Holt-Winters smoothing method. In this article the fact that the underlying model of the Holt-Winters method is a certain seasonal ARIMA is used. Minimum mean square error smoothing constants are derived and compared with those of Cipra.
LA - eng
KW - Holt-Winters method; missing observations; seasonal ARIMA model; missing observations; seasonal ARIMA model; Holt-Winters method
UR - http://eudml.org/doc/32936
ER -

References

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  1. 10.2307/1403258, International Statistical Review 54 (1986), 51–66. (1986) MR0959652DOI10.2307/1403258
  2. Statistical Methods for Forecasting, Wiley, New York, 1983. (1983) MR0719535
  3. 10.1002/for.3980080204, Journal of Forecasting 8 (1989), 97–116. (1989) DOI10.1002/for.3980080204
  4. Time Series Theory and Methods, Springer, New York, 1991. (1991) MR1093459
  5. Holt-Winters method with missing observations, Management Science. 
  6. 10.1287/mnsc.32.4.499, Management Science 32 (1986), 499–510. (1986) DOI10.1287/mnsc.32.4.499

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