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Modelling the non-stationary unconstrained bivariate integer-valued autoregressive of order 1 (NSUBINAR(1)) model is challenging due to the complex cross-correlation relationship between the counting series. Hence, this paper introduces a novel non-stationary unconstrained BINAR(1) with geometric marginals (NSUBINAR(1)GEOM) based on the assumption that the counting series are both influenced by the same time-dependent explanatory variables. The generalized quasi-likelihood (GQL) estimation method is used to estimate the regression and dependence parameters. Monte Carlo simulations and an application to a real-life accident series data are presented.

This paper introduces a new bivariate integer-valued autoregressive of order (1) (BINAR(1)) model with negative binomial (NB) innovations under non-stationary moments. The purpose of this time series process is mainly to model series that are affected by time-dependent covariate effects and that, in particular, exhibit different levels of over-dispersion which is a phenomenon commonly noticed in many real-life series applications. In this proposed model, the cross-correlation is induced locally by allowing the current counting series observation to relate with the previous-lagged observation of the other series or vice versa while the pair of NB innovations are assumed uncorrelated. The estimation of the regression, over-dispersion and dependence parameters is conducted using a generalized quasi-likelihood (GQL) approach since the specification of the likelihood function, under non-stationarity, is rather difficult to specify in the above situation. Monte-Carlo simulation experiments are executed to assess the quality of the GQL estimators. The model is also applied and compared with other bivariate time series models to some real-life series in Mauritius. [ABSTRACT FROM AUTHOR]

In spatial count data analysis, modeling with a multilateral lattice structure presents some important challenges. They include both the model construction and the estimation of the model parameters, since the structure accommodates the left, right, top, bottom, and diagonal site effects. Thus, the multilateral spatial process unifies all the popular spatial subclasses that include the unilateral, Rook, Bishop, and Queen models and, hence, makes it suitable for a wide variety of applications. This paper introduces a first‐order multilateral integer‐valued spatial process, based on a binomial thinning mechanism and some innovation term, under both stationary and nonstationary conditions. The estimation of parameters is handled by the conditional maximum likelihood estimation (CML) approach. Simulation experiments are implemented to assess the consistency of the CML estimators in the stationary and nonstationary multilateral spatial model and its subclasses, based on different grid sizes and under both covariate and noncovariate designs. The proposed model, along with its subclasses are applied to real datasets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model ( P I N M A S (q)) with Generalized Poisson and Negative Binomial innovation process, for modelling different types of dispersion in count time series. Some probabilistic properties of the process are obtained. Furthermore, the time reversibility of the model is discussed in detail. The estimation of the underlying parameters is obtained by the Conditional Least Squares method (CLS). A simulation study is carried out to evaluate the performance of the estimation method. Finally, an application on real data set is provided to show the ability of the model for fitting data. [ABSTRACT FROM AUTHOR]

We consider models for count variables with a GARCH-type structure. Such a process consists of an integer-valued component and a volatility process. Using arguments for contractive Markov chains we prove that this bivariate process has a unique stationary regime. Furthermore, we show absolute regularity (β-mixing) with geometrically decaying coefficients for the count process. These probabilistic results are complemented by a statistical analysis and a few simulations. [ABSTRACT FROM AUTHOR]

The article introduces a first-order bivariate integer-valued moving average process (BINMA(1)) where the respective innovation series are marginally COM-Poisson distributed under nonstationary moments. The purpose of this process is to model inter-related INMA(1) time series that are known to exhibit different levels and types of dispersion. The unknown parameters of the model are estimated by the Generalized Quasi-likelihood (GQL) approach. Simulation experiments and a real-life data application to intra-day stock series of two banking companies is presented. [ABSTRACT FROM AUTHOR]

This paper focuses on the modeling of the intra-day transactions at the Stock Exchange Mauritius (SEM) of the two major banking companies: Mauritius Commercial Bank Group Limited (MCB) and State Bank of Mauritius Holdings Ltd (SBMH) in Mauritius using a flexible non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) process with negative binomial (NB) innovations that may cater for different levels of over-dispersion. The generalized quasi-likelihood (GQL) approach is used to estimate the regression, dependence and over-dispersion effects. However, for the over-dispersion parameters, the auto-covariance structure in the GQL is constructed using some higher order moments. This new model is tested over some Monte-Carlo experiments and is applied to analyze the inter-related intra-day series of volume of stocks for the two banking institutions using data collected from 3 August to 16 October 2015 in the presence of some time-varying covariates such as the news effect, Friday effect and time of the day effect. [ABSTRACT FROM AUTHOR]