Smooth-transition autoregressive models for time series of bounded counts

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.

Keywords:

• Binomial STAR model
• count time series
• maximum likelihood estimation
• non-linear dependence
• self-exciting threshold
• state dependence

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.