Abstract

This paper addresses the coherent forecasting problem for overdispersed integer-valued autoregressive (INAR) model of order one having negative binomial marginal distribution. INAR models with Poisson or geometric marginal distribution have been used by several researchers to tackle the forecasting and related issues in low count time series. However, when the process results in relatively higher counts with overdispersion, these models do not provide satisfactory fit and good forecasts. We use negative binomial INAR(1) (NBINAR(1)) model for forecasting the count time series by deriving its exact forecast distribution. Extensive simulation study has been carried out to assess the performance of the forecasts obtained using NBINAR(1) with its INAR(1) counterparts. Two real data sets have been analyzed using the proposed methodology.

摘要

本文解决了具有负二项式边际分布的一阶过分散整数值自回归 (INAR) 模型的相干预测问题。一些研究人员已使用具有泊松或几何边际分布的 INAR 模型来解决低计数时间序列中的预测和相关问题。然而，当该过程导致相对较高的计数且过度分散时，这些模型无法提供令人满意的拟合和良好的预测。我们使用负二项式 INAR(1) (NBINAR(1)) 模型通过推导其精确的预测分布来预测计数时间序列。已经进行了广泛的模拟研究，以评估使用 NBINAR(1) 及其 INAR(1) 对应项获得的预测的性能。使用所提出的方法分析了两个真实数据集。