A Management Method of Multi-Granularity Dimensions for Spatiotemporal Data

To understand the complex phenomena in social space and monitor the dynamic changes in people's tracks, we need more cross-scale data. However, when we retrieve data, we often ignore the impact of multi-scale, resulting in incomplete results. To solve this problem, we proposed a management method of multi-granularity dimensions for spatiotemporal data. This method systematically described dimension granularity and the fuzzy caused by dimension granularity, and used multi-scale integer coding technology to organize and manage multi-granularity dimensions, and realized the integrity of the data query results according to the correlation between the different scale codes. We simulated the time and band data for the experiment. The experimental results showed that: (1) this method effectively solves the problem of incomplete query results of the intersection query method. (2) Compared with traditional string encoding, the query efficiency of multiscale integer encoding is twice as high. (3) The proportion of different dimension granularity has an impact on the query effect of multi-scale integer coding. When the proportion of fine-grained data is high, the advantage of multi-scale integer coding is greater.

Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probability-generating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.

An INAR(1) Time Series Model via a Modified Discrete Burr–Hatke with Medical Applications

This paper introduces a flexible discrete transmuted record type discrete Burr–Hatke (TRT-DBH) model that seems suitable for handling over-dispersion and equi-dispersion in count data analysis. Further to the elegant properties of the TRT-DBH, we propose, in the time series context, a first-order integer-valued autoregressive process with TRT-DBH distributed innovations [TRBH-INAR(1)]. The moment properties and inferential procedures of this new INAR(1) process are studied. Some Monte Carlo simulation experiments are executed to assess the consistency of the parameters of the TRBH-INAR(1) model. To further motivate its purpose, the TRBH-INAR(1) is applied to analyze the series of the COVID-19 deaths in Netherlands and the series of infected cases due to the Tularaemia disease in Bavaria. The proposed TRBH-INAR(1) model yields superior fitting criteria than other established competitive INAR(1) models in the literature. Further diagnostics related to the residual analysis and forecasting based on the TRBH-INAR(1) model are also discussed. Based on modified Sieve bootstrap predictors, we provide integer forecasts of future death of COVID-19 and infected of Tularemia.