Zero-Modified Skellam Integer-Valued GARCH Model

The Skellam distribution is a discrete distribution defined on Z. Recently, INGARCH models based on the Skellam and modified Skellam distributions have been proposed. In this paper, a ZMSINGARCH model based on the zero-modified Skellam (ZMS) distribution is proposed. This model takes into account an additional parameter to handle the integer 0 in detail, and has a reasonable explanation for the zero inflation or zero deflation ratio in order to fit the data better and capture volatility in non-zeromean time series. The definition and statistical properties of the model are given when the order p = 1 and q = 1, and numerical simulations show that the conditional maximum likelihood estimation is superior to the conditional least square estimation. The modified model is tested based on the log-likelihood ratio test statistic, and two examples from different stock trading markets are analyzed to show that the proposed model has a better performance.