The authors consider the model Zt=Σkab22iÅ=1ø(i,j)ZtÅ-i+at(j) when [ZtÅ-1,ZtÅ-2,...,ZtÅ-k]'∈R(j), where ∈R(j);1∈j∈𝓁∈ is a partition of <∼k, and for each 1∈j∈𝓁,∈at(j);t∈0∈ are i.i.d. zero-mean random variables, having a strictly positive density. Sufficient conditions are obtained for this process to be transient. In addition, for a particular class of such models, necessary and sufficient conditions for ergodicity are obtained. Least-squares estimators of the parameters are obtained and are, under mild regularity conditions, shown to be strongly consistent and asymptotically normal.
