标题： 模型系数和创新分布的联合半参数INAR自助推断 显示英文标题

标题： Joint semi-parametric INAR bootstrap inference for model coefficients and innovation distribution

摘要： 为了对计数时间序列中的序列依赖进行建模，文献中提出了各种方法。 特别是基于递归的、自回归类型的结构，如众所周知的整数值自回归（INAR）模型，在实践中非常受欢迎。 这种INAR模型的分布完全由自回归二项式稀释系数的向量和离散创新分布决定。 虽然这些模型的完全参数估计技术在文献中大多已涵盖，但半参数方法允许在不施加任何参数假设的情况下，对模型系数和创新分布进行一致且高效的联合估计。 尽管该估计量的极限分布已知，这在原则上使关于创新的渐近推断和INAR模型诊断成为可能，但在实际应用中却很繁琐。 在本文中，我们考虑一种相应的半参数INAR引导程序，并证明其在INAR系数估计和创新分布估计中的联合一致性。 我们讨论了不同的应用情景，包括拟合优度检验、预测推断以及计数时间序列的联合离散指数分析。 在模拟中，我们使用几种创新分布说明了半参数INAR引导程序的有限样本性能，并提供了真实数据的应用。 显示英文摘要

摘要： For modeling the serial dependence in time series of counts, various approaches have been proposed in the literature. In particular, models based on a recursive, autoregressive-type structure such as the well-known integer-valued autoregressive (INAR) models are very popular in practice. The distribution of such INAR models is fully determined by a vector of autoregressive binomial thinning coefficients and the discrete innovation distribution. While fully parametric estimation techniques for these models are mostly covered in the literature, a semi-parametric approach allows for consistent and efficient joint estimation of the model coefficients and the innovation distribution without imposing any parametric assumptions. Although the limiting distribution of this estimator is known, which, in principle, enables asymptotic inference and INAR model diagnostics on the innovations, it is cumbersome to apply in practice. In this paper, we consider a corresponding semi-parametric INAR bootstrap procedure and show its joint consistency for the estimation of the INAR coefficients and for the estimation of the innovation distribution. We discuss different application scenarios that include goodness-of-fit testing, predictive inference and joint dispersion index analysis for count time series. In simulations, we illustrate the finite sample performance of the semi-parametric INAR bootstrap using several innovation distributions and provide real-data applications.