Note on integer-valued bilinear time series models

This note reconsiders the nonnegative integer-valued bilinear processes introduced by Doukhan et al. [Doukhan, P., Latour, A., Oraichi, D., 2006. A simple integer-valued bilinear time series model. Adv. Appl. Prob. 38, 559–578]. Using a hidden Markov argument, we extend their result of the existence of a stationary solution for the INBL(1, 0, 1, 1) process to the class of superdiagonal INBL(p,q,m,n) models. Our approach also yields improved parameter restrictions for several moment conditions compared to the ones in [Doukhan, P., Latour, A., Oraichi, D., 2006. A simple integer-valued bilinear time series model. Adv. Appl. Prob. 38, 559–578].