A new integer-valued threshold autoregressive process based on modified negative binomial operator driven by explanatory variables

In this article, a new random coefficient integer-valued self-exciting threshold autoregressive process based on modified negative binomial operator is introduced. The autoregressive coefficients are driven by the explanatory variables via a logistic regression structure. Basic probabilistic and statistical properties of this process are discussed. Estimators of the unknown parameters are obtained via the conditional least squares and conditional maximum likelihood methods, as well as the asymptotic properties. The nonlinearity test of the proposed model and the existence test of explanatory variables are performed using the Wald-type test. Monte Carlo simulations are provided to illustrate the finite-sample performance of the estimators and the hypothesis tests. A real example is applied to illustrate the superiority of the proposed model.