A new integer--valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. This process family provides a flexible modelling framework for count data, allowing for under and over--dispersion, asymmetry, and excess of kurtosis and includes standard INAR models such as Generalized Poisson and Negative Binomial as special cases. We show that the GLK--INAR process is discrete semi--self--decomposable, infinite divisible, stable by aggregation and provides stationarity conditions. Some extensions are discussed, such as the Markov--Switching and the zero--inflated GLK--INARs. A Bayesian inference framework and an efficient posterior approximation procedure are introduced. The proposed models are applied to 130 time series from Google Trend, which proxy the worldwide public concern about climate change. New evidence is found of heterogeneity across time, countries and keywords in the persistence, uncertainty, and long--run public awareness level.

翻译：本文定义了一种具有广义拉格朗日Katz（GLK）新息的新型整数值自回归过程（INAR）。该过程族为计数数据提供了一个灵活的建模框架，能够处理欠离散与过离散、不对称性以及超额峰度等问题，并将广义泊松和负二项分布等标准INAR模型作为特例包含在内。我们证明了GLK-INAR过程具有离散半自分解性、无限可分性、聚合稳定性，并给出了其平稳性条件。文中还讨论了若干扩展模型，例如马尔可夫切换与零膨胀GLK-INAR模型。同时引入了贝叶斯推断框架及一种高效的后验近似计算方法。所提出的模型被应用于来自谷歌趋势的130个时间序列数据，这些数据反映了全球公众对气候变化关注度的动态变化。研究发现了新的证据，表明在持续性、不确定性及长期公众认知水平方面，不同时间、国家与关键词之间存在显著的异质性。