ABSTRACT
Some classical methods of generating stationary count time series do not yield a particularly flexible suite of autocovariance structures. For example, integer autoregressive moving-average (INARMA) (Steutel and Van Harn 1979; McKenzie, 1985, 1986, 1988; Al-Osh and Alzaid 1988) and discrete autoregressive moving-average (DARMA) methods (Jacobs and Lewis, 1978a, b) cannot produce negatively correlated series at any lags. This is because mixing ratios or thinning probabilities must always lie in (0,1). Also, INARMA and DARMA models cannot generate series with long memory autocovariances.
