Time series regression models for zero-inflated proportions

Abstract

Time series of proportions are often encountered in applications such as ecology, environmental science and public health. Strategies for such data include linear regression after logistic transformation. Though easy to fit, the transformation approach renders covariate effects uninterpretable on the scale on which they were observed owing to Jensen's inequality. An alternative to the transformation approach has been to directly model the response via the beta distribution. In this paper, we extend zero-inflated beta regression models for independent proportions to time series data that is bounded over the unit interval and that may take on zero values. Estimation is within the partial-likelihood framework and is computationally feasible to implement. We outline the asymptotic theory of our maximum partial likelihood estimators under mild regularity conditions and investigate their bias and variability using simulation studies. The utility of our method is illustrated using two real data examples.

Keywords:

• Autoregressive
• beta distribution
• partial-likelihood
• randomized quantile residual
• regression
• zero-inflation

Mathematics Subject Classifications:

• 62M10
• 62F10
• 62F12
• 62F03
• 62P12

Acknowledgements

The authors are very grateful to the Associate Editor and two anonymous referees for their comments and questions which have led to significant improvements of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author gratefully acknowledges support from a University of Winnipeg Major Research Grant and from Natural Sciences and Engineering Research Council of Canada.