It is known that there is a one-to-one correspondence between stationary ARMAX and state space models. In order to estimate these it is necessary first to identify and further, having identified, to choose parameters. This paper discusses the properties a system of identification and parameterization might be desired to have in relation to various examples of identification. It also constructs a (known) canonical state space form (identification) out of the constants needed to specify the corresponding ARMAX form. It is argued that what is here called "simple identification" will be the best basis for identification even though some structures cannot be identified in this manner.