Random Rounded Integer-valued Autoregressive Conditional Heteroskedastic Process

The statistical analysis of discrete variate time series has mainly concentrated on the parametric models, that is the conditional probability density function is supposed to belong to a parametric family. In general, these parameter models impose strong assumptions between the conditional mean and variance. In this paper,these parametric models are enumerated and the characters of these models are stated. The adadvantages and the disadvantages are evaluated.Random rounded integer-valued autoregressive conditional heteroskedastic processes essentially have no assumptions on the relationship between the conditional mean and variance.This is a kind of more flexible semiparametric model.Several advantages of RRINARCH models are listed in this paper:(a)negative values both for the series and its autocorrelation function are allowed;(b)its autocorrelation structure is as same as a standard autoregressive(AR) process;(c)it provides a continuous semiparametric framework for discrete variate time series, and the conditional mean and variance can be modeled separately;(d)standard software is directly applicable for its estimation.This paper lists several characters of the model:conditions for stationarity, ergodicity and the existence of moments,the consistency and asymptotic normality of the conditional least squares estimator.The conditional heteroskedastic assumption isWe propese more general assumptions and consider a new conditional heteroskedastic assumptionSimulation experiments are carried out to evaluate the new model.