High Frequency Data and A Review on INMA Integer-valued Model Class and Further Development

Abstract

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 microstructure is given. The single thing that most visibly makes the INMA model class different from its continuous variable MA counterpart is that multiplication of variables with real valued parameters is no longer 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. In this paper, 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.