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.

The balanced discrete triplet Lindley model and its INAR(1) extension: properties and COVID-19 applications.

This paper proposes a new flexible discrete triplet Lindley model that is constructed from the balanced discretization principle of the extended Lindley distribution. This model has several appealing statistical properties in terms of providing exact and closed form moment expressions and handling all forms of dispersion. Due to these, this paper explores further the usage of the discrete triplet Lindley as an innovation distribution in the simple integer-valued autoregressive process (INAR(1)). This subsequently allows for the modeling of count time series observations. In this context, a novel INAR(1) process is developed under mixed Binomial and the Pegram thinning operators. The model parameters of the INAR(1) process are estimated using the conditional maximum likelihood and Yule-Walker approaches. Some Monte Carlo simulation experiments are executed to assess the consistency of the estimators under the two estimation approaches. Interestingly, the proposed INAR(1) process is applied to analyze the COVID-19 cases and death series of different countries where it yields reliable parameter estimates and suitable forecasts via the modified Sieve bootstrap technique. On the other side, the new INAR(1) with discrete triplet Lindley innovations competes comfortably with other established INAR(1)s in the literature.

Modeling Medical Data by Flexible Integer-Valued AR(1) Process with Zero-and-One-Inflated Geometric Innovations

In this paper, we introduce a new stationary first-order integer-valued autoregressive process (INAR) with zero-and-one-inflated geometric innovations that is useful for modeling medical practical data. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares and maximum likelihood estimators are proposed to estimate the model parameters. The performance of the estimation methods is assessed by some Monte Carlo simulation experiments. The zero-and-one-inflated INAR process is subsequently applied to analyze two medical series that include the number of new COVID-19-infected series from Barbados and Poliomyelitis data. The proposed model is compared with other popular competing zero-inflated and zero-and-one-inflated INAR models on the basis of some goodness-of-fit statistics and selection criteria, where it shows to provide better fitting and hence can be considered as another important commendable model in the class of INAR models.

Re-analyzing the SARS-CoV-2 series using an extended integer-valued time series models: A situational assessment of the COVID-19 in Mauritius.

This paper proposes some high-ordered integer-valued auto-regressive time series process of order p (INAR(p)) with Zero-Inflated and Poisson-mixtures innovation distributions, wherein the predictor functions in these mentioned distributions allow for covariate specification, in particular, time-dependent covariates. The proposed time series structures are tested suitable to model the SARs-CoV-2 series in Mauritius which demonstrates excess zeros and hence significant over-dispersion with non-stationary trend. In addition, the INAR models allow the assessment of possible causes of COVID-19 in Mauritius. The results illustrate that the event of Vaccination and COVID-19 Stringency index are the most influential factors that can reduce the locally acquired COVID-19 cases and ultimately, the associated death cases. Moreover, the INAR(7) with Zero-inflated Negative Binomial innovations provides the best fitting and reliable Root Mean Square Errors, based on some short term forecasts. Undeniably, these information will hugely be useful to Mauritian authorities for implementation of comprehensive policies.

Studying the trend of the novel coronavirus series in Mauritius and its implications.

Mauritius stands as one of the few countries in the world to have controlled the current pandemic, the novel coronavirus 2019 (COVID-19) to a significant extent in a relatively short lapse of time. Owing to uncertainties and crisis amid the pandemic, as an emergency announcement, the World Health Organization (WHO) solicits the help of health authorities, especially, researchers to conduct in-depth research on the evolution and treatment of COVID-19. This paper proposes an integer-valued time series model to analyze the series of COVID-19 cases in Mauritius wherein the corresponding innovation term accommodates for covariate specification. In this set-up, sanitary curfew followed by sanitization and sensitization campaigns, time factor and safe shopping guidelines have been tested as the most significant variables, unlike climatic conditions. The over-dispersion estimates and the serial auto-correlation parameter are also statistically significant. This study also confirms the presence of some unobservable effects like the pathological genesis of the novel coronavirus and environmental factors which contribute to rapid propagation of the zoonotic virus in the community. Based on the proposed COM-Poisson mixture models, we could predict the number of COVID-19 cases in Mauritius. The forecasting results provide satisfactory mean squared errors. Such findings will subsequently encourage the policymakers to implement strict precautionary measures in terms of constant upgrading of the current health care and wellness system and re-enforcement of sanitary obligations.