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In this article, we introduce an extended binomial AR(1) model based on the generalized binomial thinning operator. This operator relaxes the independence assumption of the binomial thinning operator and contains dependent Bernoulli counting series. The new model contains the binomial AR(1) model as a particular case. Some probabilistic and statistical properties are explored. Estimators of the model parameters are derived by conditional maximum likelihood (CML), conditional least squares (CLS) and weighted conditional least squares (WCLS) methods. Some asymptotic properties and numerical results of the estimators are studied. The good performance of the new model is illustrated, among other competitive models in the literature, by an application to the monthly drunken driving counts. [ABSTRACT FROM AUTHOR]

In this article, the problem of interest is testing the conditional heteroscedasticity of Poisson autoregressive model. We construct a non parametric test statistic based on empirical likelihood method. The asymptotic distribution of the proposed statistic is derived and its finite-sample property is examined through Monte Carlo simulations. The simulation results show that the proposed method is good for practical use. [ABSTRACT FROM PUBLISHER]

In this paper, we propose several approaches to estimate the parameters of the periodic first-order integer-valued autoregressive process with period T (PINAR(1)T) in the presence of missing data. By using incomplete data, we propose two approaches that are based on the conditional expectation and conditional likelihood to estimate the parameters of interest. Then we study three kinds of imputation methods for the missing data. The performances of these approaches are compared via simulations. [ABSTRACT FROM AUTHOR]

A generalized random coefficient first-order integer-valued autoregressive process with signed thinning operator is introduced, this kind of process is appropriate for modeling negative integer-valued time series. Strict stationarity and ergodicity of process are established. Estimators of the parameters of interest are derived and their properties are studied via simulation. At last, we use bootstrap method in the real data analysis. [ABSTRACT FROM AUTHOR]

This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation. [ABSTRACT FROM AUTHOR]

We propose a new integer-valued time series process, called generalized pth-order random coefficient integer-valued autoregressive process with signed thinning operator. This kind of process is appropriate for modeling negative integer-valued time series; strict stationarity and ergodicity of the process are established. Estimators of the model's parameters are derived and their properties are studied via simulation. We apply our process to a real data example. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of estimating the volatility function of a parametric AR(1) model with nonparametric ARCH(1) errors. Consistency and asymptotic normality of local constant and local log-linear estimators are established. Our simulation study and an application to finance lead to superior performance of the local log-linear estimator compared with the conventional treatments in the literature. A possible extension of the estimation procedure is described. [ABSTRACT FROM AUTHOR]