The asymmetric power GARCH model for the volatility was introduced in 1993 in order to deal with asymmetric responses in the volatility when analyzing continuous-valued financial time series. Furthermore, asymmetric responses in the volatility also exist in nonnegative integer-valued or \(\mathbb {Z}\) -valued time series. An asymmetric power autoregressive conditional Poisson model for analyzing time series of counts has been proposed. As for another type of discrete data, GJR-GARCH models which use Poisson distribution and shifted geometric distribution as the underlying conditional distributions for \(\mathbb {Z}\) -valued time series have also been studied. Moreover, there exists a zero-inflation phenomenon, then a zero-inflated Poisson INGARCH model has been proposed for time series of counts to model this phenomenon. Combining the data features mentioned above, we propose a zero-inflated Poisson asymmetric power GARCH model for \(\mathbb {Z}\) -valued time series. Some probabilistic and statistical properties of the proposed model are provided, meanwhile, the unknown parameters are estimated in terms of the maximum likelihood method, then the asymptotic normality of the corresponding estimator is given. To demonstrate the estimation method, a simulation study is presented. A real-data example based on the daily stock returns divided by tick price is taken into account to illustrate the superiority of the new model compared with existing models.
