Integer‐valued asymmetric garch modeling
针对存在条件异方差的不相关整数值时间序列，提出一个GARCH模型，允许正负观测值对条件方差产生非对称影响，并给出平稳性、遍历性、矩存在条件及极大似然估计的渐近分布。
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.