New zero-inflated GARMA model with gamma and inverse Gaussian distributions to analyze rainfall time series

In this work, we propose zero-inflated generalized autoregressive and moving average models for continuous non-negative data with the gamma and the inverse Gaussian model distributions. The probability of zeros is also modeled depending on a logistic function of explanatory variables, including lagged terms. We propose that the autocorrelations are related only with the positive observations, including autoregressive and moving average terms corresponding only to the last positive lagged values. Another relevant innovation was the inclusion of lagged terms in the probability of zero occurrence, which reduced the autocorrelation of the randomized quantile residuals. The model was estimated by conditional maximum likelihood, presenting the conditional score function, Fisher information matrix, and the complete residual analysis. A simulation study was carried out to evaluate the estimation for different sample sizes. The real time series of daily rainfall in the city of Sao Paulo from 2008 to 2020 was analyzed, detecting a significant downwards trend of 2.8\% per year.