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Forecast horizon aggregation in integer autoregressive moving average (INARMA) models

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  • Mohammadipour, Maryam
  • Boylan, John E.

Abstract

This paper addresses aggregation in integer autoregressive moving average (INARMA) models. Although aggregation in continuous-valued time series has been widely discussed, the same is not true for integer-valued time series. Forecast horizon aggregation is addressed in this paper. It is shown that the overlapping forecast horizon aggregation of an INARMA process results in an INARMA process. The conditional expected value of the aggregated process is also derived for use in forecasting. A simulation experiment is conducted to assess the accuracy of the forecasts produced by the aggregation method and to compare it to the accuracy of cumulative h-step ahead forecasts over the forecasting horizon. The results of an empirical analysis are also provided.

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  • Mohammadipour, Maryam & Boylan, John E., 2012. "Forecast horizon aggregation in integer autoregressive moving average (INARMA) models," Omega, Elsevier, vol. 40(6), pages 703-712.
    • Handle: RePEc:eee:jomega:v:40:y:2012:i:6:p:703-712
    DOI: 10.1016/j.omega.2011.08.008
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    1. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    4. Brannas, Kurt & Hellstrom, Jorgen & Nordstrom, Jonas, 2002. "A new approach to modelling and forecasting monthly guest nights in hotels," International Journal of Forecasting, Elsevier, vol. 18(1), pages 19-30.
    5. Keith Freeland, R. & McCabe, Brendan, 2005. "Asymptotic properties of CLS estimators in the Poisson AR(1) model," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 147-153, June.
    6. Nijman, Theo E & Palm, Franz C, 1990. "Predictive Accuracy Gain from Disaggregate Sampling in ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(4), pages 405-415, October.
    7. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
    8. Man, K. S., 2004. "Linear prediction of temporal aggregates under model misspecification," International Journal of Forecasting, Elsevier, vol. 20(4), pages 659-670.
    9. Tang, Dong, 2011. "Managing finished-goods inventory under capacitated delayed differentiation," Omega, Elsevier, vol. 39(5), pages 481-492, October.
    10. Thury, Gerhard & Witt, Stephen F., 1998. "Forecasting industrial production using structural time series models," Omega, Elsevier, vol. 26(6), pages 751-767, December.
    11. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    12. Syntetos, Aris A. & Boylan, John E., 2005. "The accuracy of intermittent demand estimates," International Journal of Forecasting, Elsevier, vol. 21(2), pages 303-314.
    13. Gomes da Silva, Carlos & Figueira, José & Lisboa, João & Barman, Samir, 2006. "An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming," Omega, Elsevier, vol. 34(2), pages 167-177, April.
    14. M. Quenouille, 1958. "Discrete autoregressive schemes with varying time-intervals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 1(1), pages 21-27, December.
    15. Ruijun Bu & Brendan McCabe & Kaddour Hadri, 2008. "Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 973-994, November.
    16. Kang, In-Bong, 2003. "Multi-period forecasting using different models for different horizons: an application to U.S. economic time series data," International Journal of Forecasting, Elsevier, vol. 19(3), pages 387-400.
    17. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
    18. Hosoda, Takamichi & Disney, Stephen M., 2006. "On variance amplification in a three-echelon supply chain with minimum mean square error forecasting," Omega, Elsevier, vol. 34(4), pages 344-358, August.
    19. Gourieroux, C. & Jasiak, J., 2004. "Heterogeneous INAR(1) model with application to car insurance," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 177-192, April.
    20. R H Teunter & L Duncan, 2009. "Forecasting intermittent demand: a comparative study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(3), pages 321-329, March.
    21. Peter Neal & T. Subba Rao, 2007. "MCMC for Integer‐Valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 92-110, January.
    22. Paulo Teles & William W. S. Wei, 2002. "The Use of Aggregate Time Series in Testing for Gaussianity," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(1), pages 95-116, January.
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    3. Kang, Yanfei & Spiliotis, Evangelos & Petropoulos, Fotios & Athiniotis, Nikolaos & Li, Feng & Assimakopoulos, Vassilios, 2021. "Déjà vu: A data-centric forecasting approach through time series cross-similarity," Journal of Business Research, Elsevier, vol. 132(C), pages 719-731.
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    5. Rostami-Tabar, Bahman & Babai, Mohamed Zied & Ducq, Yves & Syntetos, Aris, 2015. "Non-stationary demand forecasting by cross-sectional aggregation," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 297-309.
    6. Pinçe, Çerağ & Turrini, Laura & Meissner, Joern, 2021. "Intermittent demand forecasting for spare parts: A Critical review," Omega, Elsevier, vol. 105(C).
    7. Babai, M. Zied & Ali, Mohammad M. & Nikolopoulos, Konstantinos, 2012. "Impact of temporal aggregation on stock control performance of intermittent demand estimators: Empirical analysis," Omega, Elsevier, vol. 40(6), pages 713-721.
    8. Rostami-Tabar, Bahman & Disney, Stephen M., 2023. "On the order-up-to policy with intermittent integer demand and logically consistent forecasts," International Journal of Production Economics, Elsevier, vol. 257(C).
    9. Bahman Rostami‐Tabar & M. Zied Babai & Aris Syntetos & Yves Ducq, 2013. "Demand forecasting by temporal aggregation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(6), pages 479-498, September.
    10. Bahman Rostami‐Tabar & Mohamed Zied Babai & Aris Syntetos & Yves Ducq, 2014. "A note on the forecast performance of temporal aggregation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(7), pages 489-500, October.
    11. Boylan, John E. & Babai, M. Zied, 2016. "On the performance of overlapping and non-overlapping temporal demand aggregation approaches," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 136-144.
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