Exponential smoothing and resampling techniques in time series prediction

Maria Manuela Neves; Clara Cordeiro

Discussiones Mathematicae Probability and Statistics (2010)

  • Volume: 30, Issue: 1, page 87-101
  • ISSN: 1509-9423

Abstract

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Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are based on the concept of exponential smoothing. There are a variety of methods that fall into the exponential smoothing family, each having the property that forecasts are weighted combinations of past observations. But time series analysis needs proper statistical modeling. The model that better describes the behavior of the series in study can be crucial in obtaining 'good' forecasts. Departures from the true underlying distribution can adversely affect those forecasts. Resampling techniques have been considered in many situations to overcome that difficulty. For time series, several authors have proposed bootstrap methodologies. Here we will present an automatic procedure built in R language that first selects the best exponential smoothing model (among a set of possibilities) for fitting the data, followed by a bootstrap approach for obtaining forecasts. A real data set has been used to illustrate the performance of the proposed procedure.

How to cite

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Maria Manuela Neves, and Clara Cordeiro. "Exponential smoothing and resampling techniques in time series prediction." Discussiones Mathematicae Probability and Statistics 30.1 (2010): 87-101. <http://eudml.org/doc/277041>.

@article{MariaManuelaNeves2010,
abstract = {Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are based on the concept of exponential smoothing. There are a variety of methods that fall into the exponential smoothing family, each having the property that forecasts are weighted combinations of past observations. But time series analysis needs proper statistical modeling. The model that better describes the behavior of the series in study can be crucial in obtaining 'good' forecasts. Departures from the true underlying distribution can adversely affect those forecasts. Resampling techniques have been considered in many situations to overcome that difficulty. For time series, several authors have proposed bootstrap methodologies. Here we will present an automatic procedure built in R language that first selects the best exponential smoothing model (among a set of possibilities) for fitting the data, followed by a bootstrap approach for obtaining forecasts. A real data set has been used to illustrate the performance of the proposed procedure.},
author = {Maria Manuela Neves, Clara Cordeiro},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {time series; bootstrap; exponential smoothing; forecasting; accuracy measures},
language = {eng},
number = {1},
pages = {87-101},
title = {Exponential smoothing and resampling techniques in time series prediction},
url = {http://eudml.org/doc/277041},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Maria Manuela Neves
AU - Clara Cordeiro
TI - Exponential smoothing and resampling techniques in time series prediction
JO - Discussiones Mathematicae Probability and Statistics
PY - 2010
VL - 30
IS - 1
SP - 87
EP - 101
AB - Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are based on the concept of exponential smoothing. There are a variety of methods that fall into the exponential smoothing family, each having the property that forecasts are weighted combinations of past observations. But time series analysis needs proper statistical modeling. The model that better describes the behavior of the series in study can be crucial in obtaining 'good' forecasts. Departures from the true underlying distribution can adversely affect those forecasts. Resampling techniques have been considered in many situations to overcome that difficulty. For time series, several authors have proposed bootstrap methodologies. Here we will present an automatic procedure built in R language that first selects the best exponential smoothing model (among a set of possibilities) for fitting the data, followed by a bootstrap approach for obtaining forecasts. A real data set has been used to illustrate the performance of the proposed procedure.
LA - eng
KW - time series; bootstrap; exponential smoothing; forecasting; accuracy measures
UR - http://eudml.org/doc/277041
ER -

References

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  1. [1] A.M. Alonso, D. Peña and J. Romo, Forecasting time series with sieve bootstrap, Journal of Statistical Planning and Inference 100 (2002), 1-11. Zbl1007.62077
  2. [2] R.G. Brown, Statistical Forecasting for inventory control, New York, McGraw-Hill 1959. Zbl0095.14606
  3. [3] P. Bühlmann, Sieve bootstrap for time series, Bernoulli 3 (1997), 123-148. Zbl0874.62102
  4. [4] The Analysis of Time Series. An Introduction, 6th ed. Chapman & Hall 2004. 
  5. [5] C. Cordeiro and M.M. Neves, The Bootstrap methodology in time series forecasting, In 'Proceedings of CompStat2006' (J. Black and A. White, Eds.), Springer Verlag (2006), 1067-1073. 
  6. [6] C. Cordeiro and M.M. Neves, The Bootstrap prediction intervals: a case-study, In 'Proceedings of the 22nd International Workshop on Statistical Modelling (IWSM2007)' (J. Castillo, A. Espinal and P. Puig, Eds.), Springer Verlag (2007), 191-194. 
  7. [7] C. Cordeiro and M.M. Neves, Bootstrap and exponential smoothing working together in forecasting time series, In 'Proceedings in Computational Statistics (COMPSTAT 2008)' (Paula Brito, Editor), Physica-Verlag (2008), 891-899. 
  8. [8] C. Cordeiro and M.M. Neves, Forecasting time series with Boot.EXPOS procedure, REVSTAT, 7:2 (2009), 135-149. 
  9. [9] E.S. Gardner, Exponential smoothing: the state of the art, J. of Forecasting, 4 (1985), 1-38. 
  10. [10] E.S. Gardner and E. Mckenzie, Forecasting trends in time series, Management Science 31 (1985), 1237-1246. Zbl0617.62105
  11. [11] C. Holt, Forecasting seasonals and trends by exponentially weighted averages, O.N.R. Memorandum 52/1957, Carnegie Institute of Technology 1957. 
  12. [12] R. Hyndman, A. Koehler, R. Snyder and S. Grose, A state framework for automatic forecasting using exponential smoothing methods, International Journal of Forecasting 18 (2002), 439-454. 
  13. [13] R. Hyndman, A. Koehler, J. Ord and R. Snyder, Forecasting with Exponential Smoothing: The State Space Approach, Springer-Verlag Inc 2008. Zbl1211.62165
  14. [14] C.C. Pegels, Exponential smoothing: some new variations, Management Science 12 (1969), 311-315. 
  15. [15] R Development Core Team, R: A language and enviroment for statistical computing, R Foundation for statistical computing, Vienna, Austria 2008. http://CRAN.R-project.org. 
  16. [16] J.W. Taylor, Exponential smoothing with a damped multiplicative trend, International Journal of ForecastingManagement Science 19 (2003), 273-289. 
  17. [17] P.R. Winters, Forecasting sales by exponentially weighted moving averages, Management Science 6 (1960), 349-362. Zbl0995.90562

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