Forecasting correlated time series with exponential smoothing models
This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters' model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.
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- Peter R. Winters, 1960. "Forecasting Sales by Exponentially Weighted Moving Averages," Management Science, INFORMS, vol. 6(3), pages 324-342, April.
- J. Bermúdez & J. Segura & E. Vercher, 2008. "SIOPRED: a prediction and optimisation integrated system for demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 258-271, December.
- Bermúdez, José D. & Corberán-Vallet, Ana & Vercher, Enriqueta, 2009. "Multivariate exponential smoothing: A Bayesian forecast approach based on simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1761-1769.
- Phillip G. Enns & Joseph A. Machak & W. Allen Spivey & William J. Wrobleski, 1982. "Forecasting Applications of an Adaptive Multiple Exponential Smoothing Model," Management Science, INFORMS, vol. 28(9), pages 1035-1044, September.
- Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
- Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
- Rob Hyndman & Muhammad Akram & Blyth Archibald, 2008. "The admissible parameter space for exponential smoothing models," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(2), pages 407-426, June.
- Forbes, C.S. & Snyder, R.D. & Shami, R.S., 2000. "Bayesian Exponential Smoothing," Monash Econometrics and Business Statistics Working Papers 7/00, Monash University, Department of Econometrics and Business Statistics.
- Gould, Phillip G. & Koehler, Anne B. & Ord, J. Keith & Snyder, Ralph D. & Hyndman, Rob J. & Vahid-Araghi, Farshid, 2008. "Forecasting time series with multiple seasonal patterns," European Journal of Operational Research, Elsevier, vol. 191(1), pages 207-222, November.
- David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
- Fernandez, F Javier & Harvey, Andrew C, 1990. "Seemingly Unrelated Time Series Equations and a Test for Homogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 71-81, January.
- Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002.
"A state space framework for automatic forecasting using exponential smoothing methods,"
International Journal of Forecasting,
Elsevier, vol. 18(3), pages 439-454.
- Hyndman, R.J. & Koehler, A.B. & Snyder, R.D. & Grose, S., 2000. "A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods," Monash Econometrics and Business Statistics Working Papers 9/00, Monash University, Department of Econometrics and Business Statistics.
- Ashton de Silva & Rob J. Hyndman & Ralph D. Snyder, 2007. "The vector innovation structural time series framework: a simple approach to multivariate forecasting," Monash Econometrics and Business Statistics Working Papers 3/07, Monash University, Department of Econometrics and Business Statistics.
- Koehler, A.B. & Snyder, R.D. & Ord, J.K., 1999.
"Forecasting Models and Prediction Intervals for the Multiplicative Holt-Winters Method,"
Monash Econometrics and Business Statistics Working Papers
1/99, Monash University, Department of Econometrics and Business Statistics.
- Koehler, Anne B. & Snyder, Ralph D. & Ord, J. Keith, 2001. "Forecasting models and prediction intervals for the multiplicative Holt-Winters method," International Journal of Forecasting, Elsevier, vol. 17(2), pages 269-286.
- Griffiths, W.E., 2001. "Bayesian Inference in the Seemingly Unrelated Regressions Models," Department of Economics - Working Papers Series 793, The University of Melbourne.
- Pfeffermann, D. & Allon, J., 1989. "Multivariate exponential smoothing: Method and practice," International Journal of Forecasting, Elsevier, vol. 5(1), pages 83-98.
- Bermudez, J.D. & Segura, J.V. & Vercher, E., 2006. "A decision support system methodology for forecasting of time series based on soft computing," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 177-191, November.
- J. D. Bermudez & J. V. Segura & E. Vercher, 2007. "Holt-Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(9), pages 1075-1090.
- Robert, Christian P., 2007. "The Bayesian Choice: From Decision Theoretic Foundations to Computational Implementation," Economics Papers from University Paris Dauphine 123456789/1908, Paris Dauphine University.
- A. C. Harvey, 1986. "Analysis and Generalisation of a Multivariate Exponential Smoothing Model," Management Science, INFORMS, vol. 32(3), pages 374-380, March.
- Geweke, John & Whiteman, Charles, 2006. "Bayesian Forecasting," Handbook of Economic Forecasting, Elsevier.
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