Threshold autoregression analysis for finite-range time series of counts with an application on measles data

ABSTRACT

This article studies the threshold autoregression analysis for the self-exciting threshold binomial autoregressive processes. Parameters' point estimation and interval estimation problems are considered via the empirical likelihood method. A new algorithm to estimate the threshold value of the threshold model is also given. Simulation study is conducted for the evaluation of the developed approach. An application on measles data is provided to show the applicability of the method.

KEYWORDS:

• Threshold binomial autoregressive processes
• empirical likelihood
• SMLS algorithm

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The mean of each regime of the SETBAR(1) and LSETBAR(1) models is calculated by $N{\pi }_i$ (i=1,2), see [5] for details.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (Nos. 11271155, 11371168, J1310022, 11571138, 11501241, 11571051, 11301137), National Social Science Foundation of China (16BTJ020), Science and Technology Research Program of Education Department in Jilin Province for the 12th Five-Year Plan (440020031139) and Natural Science Foundation of Jilin Province (20150520053JH).