Aleksandar S. Nastić

A bivariate INAR(1) time series model with geometric marginals

Abstract In this paper we introduce a simple bivariate integer-valued time series model with positively correlated geometric marginals based on the negative binomial thinning mechanism. Some properties of the model are considered. The unknown parameters of the model are estimated using the modified conditional least squares method.

A geometric time series model with dependent Bernoulli counting series

A new stationary first‐order integer‐valued autoregressive process with geometric marginal distribution based on the generalized binomial thinning is introduced. The model involves dependent count variables. Some properties of the process are determined. A set of estimators are obtained, and their asymptotic distributions are considered. Some numerical results of the estimates are presented. Possible application of the process is discussed through the real data example.

Estimation in an Integer-Valued Autoregressive Process with Negative Binomial Marginals (NBINAR(1))

The authors consider a stationary integer-valued autoregressive process of the first order with negative binomial marginals (NBINAR(1)). A set of estimators are considered and their asymptotic distributions are derived. Some numerical results of the estimates are presented. Also, the authors discuss a possible application of the process.

A Mixed INAR(p) Model

A mixed integer‐valued autoregressive model of order p is proposed. The existence of this unique, stationary and ergodic process is proved and its autocorrelation structure and some conditional stochastic characteristics are derived. Model parameters are estimated via Yule‐Walker, conditional least squares and conditional maximum likelihood methods. Finally, possible application of the model to real data sets is considered.

A geometric time-series model with an alternative dependent Bernoulli counting series

ABSTRACT In this article, we first introduce an alternative way for construction of the generalized binomial thinning operator with dependent counting series. Some properties of this thinning operator are derived and discussed. Then, by using this thinning operator, we introduce an integer-valued time-series model with geometric marginals. Some conditional and unconditional properties of this model are derived and discussed. Some estimation methods are considered and for some of them, asymptotic properties of the obtained estimates are derived. Performances of the estimates are discussed through some simulations. Finally, a real data example is considered and the goodness-of-fit of this model is compared with the models based on the binomial, negative binomial, and dependent binomial thinning operators.

Estimation in a bivariate integer-valued autoregressive process

ABSTRACT A bivariate integer-valued autoregressive time series model is presented. The model structure is based on binomial thinning. The unconditional and conditional first and second moments are considered. Correlation structure of marginal processes is shown to be analogous to the ARMA(2, 1) model. Some estimation methods such as the Yule–Walker and conditional least squares are considered and the asymptotic distributions of the obtained estimators are derived. Comparison between bivariate model with binomial thinning and bivariate model with negative binomial thinning is given.

An INAR model with discrete Laplace marginal distributions

In this paper we rst introduce a new thinning operator and derive some of its properties. Then, by using the thinning operator we dene a new stationary time series with discrete Laplace marginal distributions with either positive or negative lag-one autocorrelation. We show that this time series is distributed as the dierence of two independent NGINAR(1) time series and, using this fact, we discuss some of its properties. The Yule-Walker estimators for the unknown parameters are derived and their asymptotic properties are discussed.

An INAR(1) model based on a mixed dependent and independent counting series

ABSTRACT A mixed integer-valued autoregressive model of order one, based on the binomial and the generalized binomial thinning operator is introduced. Geometric marginal distribution is considered. Properties of the model are analysed, unknown parameters are estimated and some numerical results of the estimates are obtained. Finally, model is applied on two real data sets and compared to some relevant models.

On Shifted Geometric INAR(1) Models Based on Geometric Counting Series

Two types of shifted geometric integer valued autoregressive models of order one (SGINAR(1)) are proposed. Both are based on the thinning operator generated by counting series of i.i.d. geometric random variables. Their correlation properties are derived and compared. Also, regression and conditional variance are considered. Nonparametric estimators of model parameters are obtained and their asymptotic characterizations are given. Finally, these two models are applied to a real-life data set and they are compared to some referent INAR(1) models.

Zero-Inflated NGINAR(1) process

ABSTRACT In this paper, we develop a zero-inflated NGINAR(1) process as an alternative to the NGINAR(1) process (Ristić, Nastić, and Bakouch 2009) when the number of zeros in the data is larger than the expected number of zeros by the geometric process. The proposed process has zero-inflated geometric marginals and contains the NGINAR(1) process as a particular case. In addition, various properties of the new process are derived such as conditional distribution and autocorrelation structure. Yule-Walker, probability based Yule-Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Forecasting performances of the model are discussed. Application to a real data set shows the flexibility and potentiality of the new model.