  A unit volume zero intelligence (ZI) model is defined and the distribution of
its L1 process is recursively described. Further, a generalized ZI (GZI) model
allowing non-unit market orders, shifts of quotes and general in-spread events
is proposed and a formula for the conditional distribution of its quotes is
given, together with a formula for price impact. For both the models, MLE
estimators are formulated and shown to be consistent and asymptotically normal.
Consequently, the estimators are applied to data of six US stocks from nine
electronic markets. It is found that more complex variants of the models,
despite being significant, do not give considerably better predictions than
their simple versions with constant intensities.
