Estimation and testing for the integer-valued threshold autoregressive models based on negative binomial thinning

Abstract

To better describe the characteristics of time series of counts such as overdispersion or structural change, in this paper, we redefines the integer-valued threshold autoregressive models based on negative binomial thinning (NBTINAR(1)) under a weaker condition that the expectation of the innovations is finite. Parameters’ point estimation and interval estimation problems are considered. A method to test the nonlinearity of the data is provided. As an illustration, we conduct a simulation study and empirical analysis of Pittsburgh crime data sets.

Keywords:

• Threshold autoregressive processes
• Change point autoregressive processes
• Negative binomial thinning
• Empirical likelihood
• Nonlinearity test

Additional information

Funding

We acknowledge the financial supported by National Natural Science Foundation of China (No. 11871028, 11731015, 11571051, 11501241), National Social Science Foundation of China (16BTJ020), Natural Science Foundation of Jilin Province (No. 20150520053JH, 20170101057JC, 20180101216JC), Program for Changbaishan Scholars of Jilin Province (2015010), and Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period (No. 2016316), Philosophy and Social Sciences Planning Project of Guangdong Province during the “13th Five-Year” Plan Period (No. GD18CYJ08).