First-Order Random Coefficient Multinomial Autoregressive Model for Finite-Range Time Series of Counts

In view of the complexity and asymmetry of finite range multi-state integer-valued time series data, we propose a first-order random coefficient multinomial autoregressive model in this paper. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares (CLS) and weighted conditional least squares (WCLS) estimators of the model parameters are derived, and their asymptotic properties are established. In simulation studies, we compare these two methods with the conditional maximum likelihood (CML) method to verify the proposed procedure. A real example is applied to illustrate the advantages of our model.

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.

On the Validity of Tests for Asymmetry in Residual-Based Threshold Cointegration Models

This paper investigates the properties of tests for asymmetric long-run adjustment which are often applied in empirical studies on asymmetric price transmissions. We show that substantial size distortions are caused by preconditioning the test on finding sufficient evidence for cointegration in a first step. The extent of oversizing the test for long-run asymmetry depends inversely on the power of the primary cointegration test. Hence, tests for long-run asymmetry become invalid in cases of small sample sizes or slow speed of adjustment. Further, we provide simulation evidence that tests for long-run asymmetry are generally oversized if the threshold parameter is estimated by conditional least squares and show that bootstrap techniques can be used to obtain the correct size.

A mixed thinning based geometric INAR(1) model

In this article a geometrically distributed integer-valued autoregressive model of order one based on the mixed thinning operator is introduced. This new thinning operator is defined as a probability mixture of two well known thinning operators, binomial and negative binomial thinning. Some model properties are discussed. Method of moments and the conditional least squares are considered as possible approaches in model parameter estimation. Asymptotic characterization of the obtained parameter estimators is presented. The adequacy of the introduced model is verified by its application on a certain kind of real-life counting data, while its performance is evaluated by comparison with two other INAR(1) models that can be also used over the observed data.

A Binomial Integer-Valued ARCH Model

We present an integer-valued ARCH model which can be used for modeling time series of counts with under-, equi-, or overdispersion. The introduced model has a conditional binomial distribution, and it is shown to be strictly stationary and ergodic. The unknown parameters are estimated by three methods: conditional maximum likelihood, conditional least squares and maximum likelihood type penalty function estimation. The asymptotic distributions of the estimators are derived. A real application of the novel model to epidemic surveillance is briefly discussed. Finally, a generalization of the introduced model is considered by introducing an integer-valued GARCH model.