Nasirzadeh R, Bakouch H
Department of Statistics, Faculty of Science, Fasa University, Fasa, Iran.
Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia.
J Appl Stat. 2024 Feb 5;51(12):2457-2480. doi: 10.1080/02664763.2023.2301321. eCollection 2024.
This study explores zero-inflated count time series models used to analyze data sets with characteristics such as overdispersion, excess zeros, and autocorrelation. Specifically, we investigate the process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric marginal distribution. Our focus is on examining various estimation and prediction techniques for this model. We employ estimation methods, including Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators for parameter estimation. Additionally, we propose forecasting approaches, such as median, Bayesian, and Sieve Bootstrap methods, to predict future values of the series. We assess the performance of these methods through simulation studies and real-world data analysis, finding that all methods perform well, providing 95% highest predicted probability intervals that encompass the observed data. While Bayesian and Bootstrap methods require more time for execution, their superior predictive accuracy justifies their use in forecasting.
本研究探讨了用于分析具有过度分散、过多零值和自相关等特征数据集的零膨胀计数时间序列模型。具体而言，我们研究了过程，这是一种具有随机系数和零膨胀几何边际分布的一阶平稳整数值自回归模型。我们的重点是研究该模型的各种估计和预测技术。我们采用估计方法，包括用于参数估计的惠特尔、锥形谱惠特尔、最大经验似然和筛法自助估计器。此外，我们提出了预测方法，如中位数、贝叶斯和筛法自助法，以预测该序列的未来值。我们通过模拟研究和实际数据分析评估这些方法的性能，发现所有方法都表现良好，提供了包含观测数据的95%最高预测概率区间。虽然贝叶斯和自助法执行需要更多时间，但其卓越的预测准确性证明了它们在预测中的应用价值。
