Chattopadhyay Subhankar, Maiti Raju, Das Samarjit, Biswas Atanu
Applied Statistics Unit Indian Statistical Institute Kolkata India.
Economic Research Unit Indian Statistical Institute Kolkata India.
Stat Neerl. 2022 Feb;76(1):4-34. doi: 10.1111/stan.12251. Epub 2021 Jul 11.
In this article, we consider the problem of change-point analysis for the count time series data through an integer-valued autoregressive process of order 1 (INAR(1)) with time-varying covariates. These types of features we observe in many real-life scenarios especially in the COVID-19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time-varying smoothing covariate. By using such model, we can model both the components in the active cases at time-point namely, (i) number of nonrecovery cases from the previous time-point and (ii) number of new cases at time-point . We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID-19 data sets and compare our proposed model with another PINAR(1) process which has time-varying covariate but no change-point, to demonstrate the overall performance of our proposed model.
在本文中，我们考虑通过具有时变协变量的一阶整值自回归过程（INAR(1)）对计数时间序列数据进行变点分析的问题。我们在许多实际场景中观察到这类特征，特别是在COVID-19数据集中，其中活跃病例数随时间先下降然后又上升。为了捕捉这些特征，我们使用具有时变平滑协变量的泊松INAR(1)过程。通过使用这样的模型，我们可以对时间点处活跃病例中的两个组成部分进行建模，即（i）上一个时间点未康复病例的数量和（ii）时间点处新病例的数量。我们研究了所提出模型的一些理论性质以及预测。进行了一些模拟研究以研究所提出方法的有效性。最后，我们分析了两个COVID-19数据集，并将我们提出的模型与另一个具有时变协变量但无变点的PINAR(1)过程进行比较，以展示我们提出模型的整体性能。
