The title is self explanatory: I am interested in which models are suitable for forecasting time series with a lot of zero values in it. Which forecasting models are recommended?
The problem you are referring to is called sparse data analysis/intermittent demand analysis.The ACF/PACF is meaningless due to the false correlation induced by consecutive 0's. One earlier method to deal with this is called Croston's Method but lacks generality to deal with unusual values and level/trend changes in the data. Level/trend changes can be observed when examining the rate data (demand/# of 0's since last demand ) where demand is the actual non-zero observation. I have implemented a robust Croston-like approach in AUTOBOX (a piece of software that I helped to develop ).