In this paper we studied a least squares estimation parameters of the Generalized Space Time AutoRegressive (GSTAR) model and its properties, especially in consistency and asymptotic normality. We use R software to estimate the GSTAR parameter and apply the model toward real phenomena of data, such as an oil production data at volcanic layer.

Information diffusion, information spread, and influencers are important concepts in many studies on social media, especially Twitter analytics. However, literature overviews on the information diffusion of Twitter analytics are sparse, especially on the use of continuous time Markov chain (CTMC). This paper examines the following topics: (1) the purposes of studies about information diffusion on Twitter, (2) the methods adopted to model information diffusion on Twitter, (3) the metrics applied, and (4) measures used to determine influencer rankings. We employed a systematic literature review (SLR) to explore the studies related to information diffusion on Twitter extracted from four digital libraries. In this paper, a two-stage analysis was conducted. First, we implemented a bibliometric analysis using VOSviewer and R-bibliometrix software. This approach was applied to select 204 papers after conducting a duplication check and assessing the inclusion–exclusion criteria. At this stage, we mapped the authors’ collaborative networks/collaborators and the evolution of research themes. Second, we analyzed the gap in research themes on the application of CTMC information diffusion on Twitter. Further filtering criteria were applied, and 34 papers were analyzed to identify the research objectives, methods, metrics, and measures used by each researcher. Nonhomogeneous CTMC has never been used in Twitter information diffusion modeling. This finding motivates us to further study nonhomogeneous CTMC as a modeling approach for Twitter information diffusion.

In December 2021, the latest COVID-19 variant, Omicron, was confirmed in Indonesia. Unlike the Delta variant, the number of deaths in the Omicron type did not increase significantly and remained constant, even though the cases increased significantly. It is hoped that Indonesia will declare COVID-19 endemic. Jakarta is the capital of Indonesia and the first city where the new COVID-19 virus emerged. Therefore, we are trying to model COVID-19 cases in Jakarta and predict future cases to see if endemic conditions are identified. We applied Neural Network Auto-Regressive (NNAR) and Long Short-Term Memory (LSTM) methods. It is found that the NNAR forecast better for positive confirmed cases with an R-squared 0.939 and the LSTM forecast better for cases of death with an R-squared 0.9337. The forecasting results for the next 7 days reveal that positive confirmed cases of COVID-19 in Jakarta will increase slightly. In addition, the death cases experienced a very small increase, only one new case. According to the results of this study, it can be concluded that COVID-19 in Jakarta will enter an endemic phase in Jakarta, with no substantial increase in cases and a low mortality rate.