A review of INMA integer-valued model class, application and further development

In this paper, we review INMA time series of integer-valued model class, and discuss its further development. These models have been developed for analyzing high frequency financial count data. A vivid description of high frequency data in the context of market micro structure is given. The most distinguishing feature that makes the INMA model class different from its continuous variable MA counterpart is that multiplication of variables with real valued parameters no longer remains a viable operation when the result is to be integer-valued. In the estimation of these models, no underlying distributions are assumed. Hence, the discussion of estimations are limited to CL, FGLS and GMM. A further development of estimation procedures for these models have also been reviewed. We suggest that the models could be estimated with Quasi Maximum Likelihood and propose in addition a Generalized Method of Moment of Quasi Maximum Likelihood. We have also discussed how INMA model class can be extended with different underlying distributions for innovations.