This study proposes a zero-inflated Rayleigh seasonal autoregressive moving average model with exogenous regressors (iRSARMAX) to model and forecast non-negative time series, accommodating the presence of zero values. The proposed iRSARMAX models the conditional mean of the continuous part of the mixture distribution by using a dynamic structure that considers stochastic seasonality, autoregressive and moving average terms, exogenous regressors, and a link function. It also models the mixture parameters related to the inflated (zero) values with a parsimonious dynamic structure. Furthermore, the analytical score vector was deduced and considered in the conditional maximum likelihood estimation of the introduced model parameters. The analytical Fisher information matrix was obtained and used for hypothesis testing and interval inferences for the parameters of the proposed model. Randomized quantile residuals were considered, and goodness-of-fit tests were implemented to validate the model. An extensive simulation study was performed to evaluate the performance of conditional likelihood inference over the model parameters for finite sample sizes. The proposed model excelled compared to the traditional seasonal autoregressive and moving average model and the Holt-Winters filtering in forecasting influent flow. In addition, it outperformed competitors in predicting synthetic aperture radar (SAR) image data.