Although many time series are realizations from discrete processes, it is often that a continuous Gaussian model is implemented for modeling and forecasting the data, resulting in incoherent forecasts. Forecasts using a Poisson-Lindley integer autoregressive (PLINAR) model are compared to variations of Gaussian forecasts via simulation by equating relevant moments of the marginals of the PLINAR to the Gaussian AR. To illustrate utility, the methods discussed are applied and compared using a discrete series with model parameters being estimated using each of conditional least squares, Yule-Walker, and maximum likelihood.

翻译：尽管许多时间序列源自离散过程，但建模与预测时通常采用连续高斯模型，这会导致非一致性预测。本研究通过模拟实验，将泊松-林德利整数自回归（PLINAR）模型的预测结果与多种高斯预测变体进行比较，方法是将PLINAR模型边缘分布的相关矩与高斯自回归模型相匹配。为说明方法实用性，将讨论的预测方法应用于离散序列进行对比分析，其中模型参数分别采用条件最小二乘法、尤尔-沃克估计法和最大似然法进行估计。