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The moments of SETARMA models

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  • Amendola, Alessandra
  • Niglio, Marcella
  • Vitale, Cosimo

Abstract

This paper considers the moments generation of the self exciting threshold autoregressive moving average model. In particular the exact form of the moments of order r is derived and, using this result, the unconditional variance, the skewness and the kurtosis index are given as functions of low-order moments. The use of the theoretical results are mainly addressed in the model selection context and some practical implications are further investigated through Monte Carlo simulations.

Suggested Citation

  • Amendola, Alessandra & Niglio, Marcella & Vitale, Cosimo, 2006. "The moments of SETARMA models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 625-633, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:6:p:625-633
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    References listed on IDEAS

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    1. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
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    Cited by:

    1. Milheiro-Oliveira, Paula, 2022. "An alternative sequential method for the state estimation of a partially observed SETAR(1) process," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Marian Vavra, 2012. "A Note on the Finite Sample Properties of the CLS Method of TAR Models," Birkbeck Working Papers in Economics and Finance 1206, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Chan, Wai-Sum, 2022. "On temporal aggregation of some nonlinear time-series models," Econometrics and Statistics, Elsevier, vol. 21(C), pages 38-49.
    4. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    5. Marcella Niglio, 2007. "Multi-step forecasts from threshold ARMA models using asymmetric loss functions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 395-410, November.
    6. Xiaobing Zheng & Kun Liang & Qiang Xia & Dabin Zhang, 2022. "Best Subset Selection for Double-Threshold-Variable Autoregressive Moving-Average Models: The Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1175-1201, March.
    7. Cathy Chen & Feng Liu & Richard Gerlach, 2011. "Bayesian subset selection for threshold autoregressive moving-average models," Computational Statistics, Springer, vol. 26(1), pages 1-30, March.
    8. Amendola, Alessandra & Christian, Francq, 2009. "Concepts and tools for nonlinear time series modelling," MPRA Paper 15140, University Library of Munich, Germany.

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