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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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