Abstract
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].
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