Nenegativni celobrojni autoregresivni procesi u slučajnoj sredini generisani geometrijskim brojačkim nizovima

Here are analyzed integer autoregressive (INAR) processes in the random environment generated by geometric counting series. Firstly, the first order random environment INAR model is introduced. Later, random environment INAR models of higher order, as well as their general form, are defined. Finally, the bivariate model based on the bivariate random process is defined. The properties of all introduced models are analyzed. Estimation of unknown parameters is given and validate on the simulated data. Model quality is confirmed by application on the real-life data, comparing results with the competitive models

Forecasting with two generalized integer-valued autoregressive processes of order one in the mutual random environment

In this article, we consider two univariate random environment integer-valued autoregressive processes driven by the same hidden process. A model of this kind is capable of describing two correlated non-stationary counting time series using its marginal variable parameter values. The properties of the model are presented. Some parameter estimators are described and implemented on the simulated time series. The introduction of this bivariate integer-valued autoregressive model with a random environment is justified at the end of the paper, where its real-life data-fitting performance was checked and compared to some other appropriate models. The forecasting properties of the model are tested on a few data sets, and forecasting errors are discussed through the residual analysis of the components that comprise the model.Peer Reviewe

CONDITIONAL LEAST SQUARES ESTIMATION OF THE PARAMETERS OF HIGHER ORDER RANDOM ENVIRONMENT INAR MODElS

Two different random environment INAR models of higher order, precisely RrNGINARmax(p) and RrNGINAR1(p), are presented as a new approach to modeling non-stationary nonnegative integer-valued autoregressive processes. The interpretation of these models is given in order to better understand the circumstances of their application to random environment counting processes. The estimation statistics, defined using the Conditional Least Squares (CLS) method, is introduced and the properties are tested on the replicated simulated data obtained by RrNGINAR models with different parameter values. The obtained CLS estimates are presented and discussed

Nenegativni celobrojni autoregresivni procesi u slučajnoj sredini generisani geometrijskim brojačkim nizovima

Here are analyzed integer autoregressive (INAR) processes in the random environment generated by geometric counting series. Firstly, the first order random environment INAR model is introduced. Later, random environment INAR models of higher order, as well as their general form, are defined. Finally, the bivariate model based on the bivariate random process is defined. The properties of all introduced models are analyzed. Estimation of unknown parameters is given and validate on the simulated data. Model quality is confirmed by application on the real-life data, comparing results with the competitive models

Forecasting with two generalized integer-valued autoregressive processes of order one in the mutual random environment

In this article, we consider two univariate random environment integer-valued autoregressive processes driven by the same hidden process. A model of this kind is capable of describing two correlated non-stationary counting time series using its marginal variable parameter values. The properties of the model are presented. Some parameter estimators are described and implemented on the simulated time series. The introduction of this bivariate integer-valued autoregressive model with a random environment is justified at the end of the paper, where its real-life data-fitting performance was checked and compared to some other appropriate models. The forecasting properties of the model are tested on a few data sets, and forecasting errors are discussed through the residual analysis of the components that comprise the model

Forecasting with two generalized integer-valued autoregressive processes of order one in the mutual random environment

In this article, we consider two univariate random environment integer-valued autoregressive processes driven by the same hidden process. A model of this kind is capable of describing two correlated non-stationary counting time series using its marginal variable parameter values. The properties of the model are presented. Some parameter estimators are described and implemented on the simulated time series. The introduction of this bivariate integer-valued autoregressive model with a random environment is justified at the end of the paper, where its real-life data-fitting performance was checked and compared to some other appropriate models. The forecasting properties of the model are tested on a few data sets, and forecasting errors are discussed through the residual analysis of the components that comprise the model