Abstract
The binomial smooth-transition autoregressive (BSTAR) model is proposed as a non-linear model for time series of bounded counts. The BSTAR(1) model enhances the first-order binomial autoregressive model by a smooth-transition mechanism between two regimes. Apart from this basic BSTAR model, also model extensions with more than two regimes, with higher-order autoregression, or with extra-binomial variation are discussed. Moreover, parameter estimation is addressed. We analyze the asymptotic and the finite-sample properties of the maximum likelihood estimator, which also covers the BSTAR’s threshold parameter. The BSTAR model is applied to two real-world data examples from the fields of epidemiology and meteorology.
Acknowledgments
The authors thank the associate editor and the two referees for their useful comments on an earlier draft of this article.
Notes
1 The full derivations are available from the authors upon request.