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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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    2. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    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. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    14. Kolassa, Stephan, 2022. "Commentary on the M5 forecasting competition," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1562-1568.

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