论文标题
具有广义Katz创新
First-order integer-valued autoregressive processes with Generalized Katz innovations
论文作者
论文摘要
定义了一个新的整数 - 可估算的自回归过程（INAR），并定义了广义的拉格朗日katz（GLK）创新。该过程家族为计数数据提供了灵活的建模框架，可用于下和过度分散，不对称和过量峰度，并包括标准的INAR模型，例如广义泊松和负二项式，作为特殊情况。我们表明，glk - inar过程是离散的半自我 - 可解释的，无限的分裂，通过聚集稳定并提供平稳性条件。讨论了一些扩展，例如马尔可夫 - 开关和零元素的glk-inars。引入了贝叶斯推理框架和有效的后近似程序。拟议的模型适用于Google趋势的130个时间序列，该趋势代表了全球公众对气候变化的关注。在持久性，不确定性和长期公众意识水平上，时间，国家和关键词之间发现了新的证据。
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.
