Despite their high socio-economic importance, forecasts of tropical rainfall on a synoptic timescale are still poor. Due to the complex nature of convection, numerical weather prediction (NWP) models struggle to deliver reliable and accurate predictions of rainfall for the tropics. For example, in a previous study, we have shown that a simple probabilistic climatology based on past observations at a given location and a given day outperforms raw ensemble precipitation forecasts from several NWP centers over West Africa. Even after the application of state-of-the-art statistical post-processing, forecasts have at best moderate skill compared to climatology. Here, we propose a new statistical method for the prediction of tropical rainfall using spatio-temporal correlations of rainfall as well as the phasing and intensity of convectively coupled equatorial waves, which have been shown to govern predictability of tropical precipitation on the synoptic timescale. The focus of this study is on predictions of the occurrence of precipitation and the probability of precipitation exceeding medium and high precipitation rates. The analyzed rainfall data are Tropical Rainfall Measuring Mission (TRMM) observations for the years 1998 to 2014. To obtain probabilistic forecasts for the occurrence of precipitation we use logistic regression models with raw and wave-filtered precipitation as predictors on top of a suitably modeled climatology. The predictors are selected in such a way that they have the highest spatio-temporal correlation with the observation. The activity of equatorial waves is filtered in the wavenumber-frequency domain. For each year the model was trained on all remaining years and verified out-of-sample for that specific year. Applied to northern tropical Africa, the new statistical model successfully forecasts precipitation probabilities and outperforms simple climatological as well as NWP forecasts. Spatio-temporal correlation patterns of raw precipitation with future rainfall can be ascribed to a mixture of influences of specific equatorial waves and the background state of the atmosphere. Over most parts of West Africa, the correlation structure mimics typical wavelengths and propagation speeds of African Easterly Waves. The forecast skill improves further if wave filtered precipitation is used as a predictor. The skill varies geographically with some regions such as the Guinea Coast showing scores up to 10% better than climatology and NWP models. This demonstrates the potential of relatively simple statistical models. We believe that this method can be also applied to other tropical regions where convectively coupled waves modulate precipitation. Particularly for tropical countries with limited computational power the statistical methods developed here can be a useful alternative to complex and expensive NWP forecasts. We are currently developing a toolkit that will semi-operationally forecast rainfall for the entire tropics.