This paper introduces a class of generalised linear models (GLMs) driven by latent processes for modelling count, real-valued, binary, and positive continuous time series. Extending earlier latent-process regression frameworks based on Poisson or one-parameter exponential family assumptions, we allow the conditional distribution of the response to belong to a bi-parameter exponential family, with the latent process entering the conditional mean multiplicatively. This formulation substantially broadens the scope of latent-process GLMs, for instance, it naturally accommodates gamma responses for positive continuous data, enables estimation of an unknown dispersion parameter via method of moments, and avoids restrictive conditions on link functions that arise under existing formulations. We establish the asymptotic normality of the GLM estimators obtained from the GLM likelihood that ignores the latent process, and we derive the correct information matrix for valid inference. In addition, we provide a principled approach to prediction and forecasting in GLMs driven by latent processes, a topic not previously addressed in the literature. We present two real data applications on measles infections in North Rhine-Westphalia (Germany) and paleoclimatic glacial varves, which highlight the practical advantages and enhanced flexibility of the proposed modelling framework.

翻译：本文提出了一类由潜在过程驱动的广义线性模型（GLM），用于建模计数、实值、二元及正连续时间序列。通过扩展先前基于泊松或单参数指数族假设的潜在过程回归框架，我们允许响应变量的条件分布属于双参数指数族，且潜在过程以乘积形式进入条件均值。这一表述显著拓宽了潜在过程GLM的适用范围：例如，它自然地适用于正连续数据的伽马响应，能够通过矩估计方法估计未知的离散参数，并避免了现有框架下对连接函数施加的限制性条件。我们证明了忽略潜在过程的GLM似然函数所得估计量的渐近正态性，并推导了适用于有效推断的正确信息矩阵。此外，我们为潜在过程驱动的GLM提供了一种基于原理的预测与预报方法，该议题在现有文献中尚未被系统探讨。通过德国北莱茵-威斯特法伦州麻疹感染数据和古气候冰川纹泥两个实际数据应用，我们展示了所提建模框架的实践优势与增强的灵活性。