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Exact Least Squares Multi‐Step Prediction From Nonlinear Autoregressive Models

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  • John. Pemberton

Abstract

. We obtain an integral equation recurrence relation for the optimal least squares predictor of a nonlinear autoregressive time series model. Numerical solutions are given for a first order threshold model up to three steps ahead.

Suggested Citation

  • John. Pemberton, 1987. "Exact Least Squares Multi‐Step Prediction From Nonlinear Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(4), pages 443-448, July.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:4:p:443-448
    DOI: 10.1111/j.1467-9892.1987.tb00007.x
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    Cited by:

    1. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    2. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415.
    3. Perez-Rodriguez, Jorge V. & Torra, Salvador & Andrada-Felix, Julian, 2005. "STAR and ANN models: forecasting performance on the Spanish "Ibex-35" stock index," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 490-509, June.
    4. Conlin Lizieri & Steven Satchell & Elaine Worzala & Roberto Dacco', 1998. "Real Interest Regimes and Real Estate Performance: A Comparison of UK and US Markets," Journal of Real Estate Research, American Real Estate Society, vol. 16(3), pages 339-356.
    5. Harvill, Jane L. & Ray, Bonnie K., 2005. "A note on multi-step forecasting with functional coefficient autoregressive models," International Journal of Forecasting, Elsevier, vol. 21(4), pages 717-727.
    6. Bontempi, Gianluca & Ben Taieb, Souhaib, 2011. "Conditionally dependent strategies for multiple-step-ahead prediction in local learning," International Journal of Forecasting, Elsevier, vol. 27(3), pages 689-699, July.
    7. De Gooijer, Jan G. & De Bruin, Paul T., 1998. "On forecasting SETAR processes," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 7-14, January.
    8. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    9. Dimitris N. Politis & Kejin Wu, 2023. "Multi-Step-Ahead Prediction Intervals for Nonparametric Autoregressions via Bootstrap: Consistency, Debiasing, and Pertinence," Stats, MDPI, vol. 6(3), pages 1-29, August.

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