The number of mass shootings in the United States has increased in the recent decades. Understanding the future risk of the mass shootings is critical for designing strategies to mitigate the risk of mass shootings, and part of understanding the future risk is to forecast the frequency or number of mass shootings in the future. Despite the increasing trend in mass shootings, they thankfully remain rare events with fewer than 10 mass shootings occurring in a single year. Limited historical data with substantial annual variability poses challenges to accurately forecasting rare events such as the number of mass shootings in the United States. Different forecasting models can be deployed to tackle this challenge. This article compares three forecasting models, a change-point model, a time series model, and a hybrid of a time series model with an artificial neural network model. Each model is applied to forecast the frequency of mass shootings. Comparing among results from these models reveals advantages and disadvantages of each model when forecasting rare events such as mass shootings. The hybrid ARIMA-ANN model can be tuned to follow variation in the data, but the pattern of the variation may not continue into the future. The mean of the change-point model and the ARIMA model exhibit much more less annual variation and are not influenced as much by the inclusion of a single data point. The insights generated from the comparison are beneficial for selecting the best model and accurately estimating the risk of mass shootings in the United States.