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Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use

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  • Wai-Sum Chan
  • Albert Wong
  • Howell Tong

Abstract

This paper introduces nonlinear threshold time series modeling techniques that actuaries can use in pricing insurance products, analyzing the results of experience studies, and forecasting actuarial assumptions. Basic “self-exciting” threshold autoregressive (SETAR) models, as well as heteroscedastic and multivariate SETAR processes, are discussed. Modeling techniques for each class of models are illustrated through actuarial examples. The methods that are described in this paper have the advantage of being direct and transparent. The sequential and iterative steps of tentative specification, estimation, and diagnostic checking parallel those of the orthodox Box-Jenkins approach for univariate time series analysis.

Suggested Citation

  • Wai-Sum Chan & Albert Wong & Howell Tong, 2004. "Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 37-61.
    • Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:37-61
    DOI: 10.1080/10920277.2004.10596170
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    Cited by:

    1. Mittnik, Stefan & Semmler, Willi, 2013. "The real consequences of financial stress," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1479-1499.
    2. Chan Wai-Sum & Hung King-Chi, 2011. "On Robust Testing and Modelling of Threshold-Type Non-Linearity in ASEAN Foreign Exchange Markets," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 5(2), pages 1-16, July.
    3. Hongyue Guo & Xiaodong Liu & Zhubin Sun, 2016. "Multivariate time series prediction using a hybridization of VARMA models and Bayesian networks," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2897-2909, December.
    4. Yaxing Yang & Shiqing Ling, 2018. "A Note On The Lse Of Three-Regime Tar Model With An Infinite Variance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 1-13, June.
    5. Fischer, Henning & Stolper, Oscar, 2019. "The nonlinear dynamics of corporate bond spreads: Regime-dependent effects of their determinants," Discussion Papers 08/2019, Deutsche Bundesbank.
    6. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.
    7. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.

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