Abstract: Aiming at the modeling problem of nonlinear integer-valued time series data with upper limit and dependent structure between data, we proposed a self-exciting generalized binomial threshold autoregressive model. Firstly, we proved the strictly stationary and ergodicity of the model, and discussed some statistical properties of the model, including the expectation, variance, aoto-covariance and the transition probability. Secondly, we gave the conditional maximum likelihood estimation method of the model parameters in the case of known and unknown threshold variable. Finally, we applied the model to a set of real data for fitting verification.

Key words: integer-valued time series, generalized binomial thinning operator, threshold autoregressive process, conditional maximum likelihood estimation