Conditional maximum likelihood estimation in negative binomial INGARCH processes with known number of successes when the true parameter is at the boundary of the parameter space

The paper establishes the asymptotic distribution of the conditional maximum likelihood estimator for integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) processes of conditional negative binomial distributions, with the number of successes in the definition of the negative binomial distribution being assumed to be known, when the true parameter is at the boundary of the parameter space. Based on the result, coefficient nullity tests are developed for model simplification. The proposed tests are investigated through a simulation study.