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CLAR(1) point forecasting under estimation uncertainty

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  • Simon Nik
  • Christian H. Weiß

Abstract

Forecast error is not only caused by the randomness of the data‐generating process but also by the uncertainty due to estimated model parameters. We investigate these different sources of forecast error for a popular type of count process, the Poisson first‐order integer‐valued autoregressive (INAR(1)) process. However, many of our analytical derivations also hold for the more general family of conditional linear AR(1) (CLAR(1)) processes. In addition, results from a simulation study are presented, to verify and complement our asymptotic approximations.

Suggested Citation

  • Simon Nik & Christian H. Weiß, 2020. "CLAR(1) point forecasting under estimation uncertainty," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 489-516, November.
    • Handle: RePEc:bla:stanee:v:74:y:2020:i:4:p:489-516
    DOI: 10.1111/stan.12206
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    References listed on IDEAS

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    1. Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2019. "Evaluating Approximate Point Forecasting of Count Processes," Econometrics, MDPI, vol. 7(3), pages 1-28, July.
    2. Brajendra C. Sutradhar, 2008. "On forecasting counts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(2), pages 109-129.
    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. Raju Maiti & Atanu Biswas & Samarjit Das, 2016. "Coherent forecasting for count time series using Box–Jenkins's AR(p) model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 123-145, May.
    5. Phillips, Peter C. B., 1979. "The sampling distribution of forecasts from a first-order autoregression," Journal of Econometrics, Elsevier, vol. 9(3), pages 241-261, February.
    6. Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.
    7. 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.
    8. Mohammadipour, Maryam & Boylan, John E., 2012. "Forecast horizon aggregation in integer autoregressive moving average (INARMA) models," Omega, Elsevier, vol. 40(6), pages 703-712.
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    Cited by:

    1. Wooi Chen Khoo & Seng Huat Ong & Biswas Atanu, 2022. "Coherent Forecasting for a Mixed Integer-Valued Time Series Model," Mathematics, MDPI, vol. 10(16), pages 1-15, August.

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