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Two-Threshold-Variable Integer-Valued Autoregressive Model

Author

Listed:
  • Jiayue Zhang

    (School of Mathematics, Jilin University, Changchun 130012, China)

  • Fukang Zhu

    (School of Mathematics, Jilin University, Changchun 130012, China)

  • Huaping Chen

    (School of Mathematics and Statistics, Henan University, Kaifeng 475004, China)

Abstract

In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some of its basic properties, including the mean, variance, strict stationarity, and ergodicity. We consider the conditional least squares (CLS) estimation and discuss the asymptotic normality of the CLS estimator under the known and unknown threshold values. The performances of the CLS estimator are compared via simulation studies. In addition, two real data sets are considered to underline the superior performance of the proposed model.

Suggested Citation

  • Jiayue Zhang & Fukang Zhu & Huaping Chen, 2023. "Two-Threshold-Variable Integer-Valued Autoregressive Model," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3586-:d:1220439
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    References listed on IDEAS

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    1. Dueker, Michael J. & Sola, Martin & Spagnolo, Fabio, 2007. "Contemporaneous threshold autoregressive models: Estimation, testing and forecasting," Journal of Econometrics, Elsevier, vol. 141(2), pages 517-547, December.
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    3. Maria Eduarda Silva & Vera Lúcia Oliveira, 2005. "Difference Equations for the Higher Order Moments and Cumulants of the INAR(p) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 17-36, January.
    4. Boero, Gianna & Marrocu, Emanuela, 2004. "The performance of SETAR models: a regime conditional evaluation of point, interval and density forecasts," International Journal of Forecasting, Elsevier, vol. 20(2), pages 305-320.
    5. Chao Wang & Heng Liu & Jian-Feng Yao & Richard A. Davis & Wai Keung Li, 2014. "Self-Excited Threshold Poisson Autoregression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 777-787, June.
    6. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    7. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
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    Cited by:

    1. Yixuan Fan & Jianhua Cheng & Dehui Wang, 2024. "A new integer-valued threshold autoregressive process based on modified negative binomial operator driven by explanatory variables," Statistical Papers, Springer, vol. 65(9), pages 5873-5901, December.

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