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<p>Non-stationary integer-valued time series of counts often come with piecewise characteristics and high autocorrelation, which brings challenges for modeling and inference. To address this issue, this article introduces a class of smooth transition integer-valued autoregressive process with signed binomial thinning operator. Basic probabilistic and statistical properties, including stationarity, ergodicity and some moments, are derived. Conditional least squares and conditional maximum likelihood estimators, together with their asymptotic properties, are developed. A nonlinearity test for a constant coefficient model against the proposed model is also proposed. Based on simulations, the model’s practical utility is demonstrated using a time series of perceptual speed test scores from schizophrenia patients.</p>

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A class of smooth transition \(\mathbb {Z}\)-valued autoregressive model with signed binomial thinning

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • Tingting Zhang,
  • Dehui Wang

摘要

Non-stationary integer-valued time series of counts often come with piecewise characteristics and high autocorrelation, which brings challenges for modeling and inference. To address this issue, this article introduces a class of smooth transition integer-valued autoregressive process with signed binomial thinning operator. Basic probabilistic and statistical properties, including stationarity, ergodicity and some moments, are derived. Conditional least squares and conditional maximum likelihood estimators, together with their asymptotic properties, are developed. A nonlinearity test for a constant coefficient model against the proposed model is also proposed. Based on simulations, the model’s practical utility is demonstrated using a time series of perceptual speed test scores from schizophrenia patients.