The problem of ergodicity, stationarity and maximum likelihood estimation is studied for binary time series models that include a latent process. General models are considered, covered by different specifications of a link function. Maximum likelihood estimation is discussed and it is shown that the MLE satisfies standard asymptotic theory. The logistic and probit models, routinely employed for the analysis of binary time series data, are of special importance in this study. The results are applied to simulated and real data.