Integer-valued asymmetric garch modeling

We propose a GARCH model for uncorrelated, integer-valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two-sided Poisson distribution with time-varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.