Forecasting the spread of COVID-19 infection is an important aspect of public health management. In this paper, we propose an approach to forecasting the spread of the pandemic based on the vector autoregressive model. Concretely, we combine the time series for the number of new cases and the number of new deaths to obtain a joint forecasting model. We apply the proposed model to forecast the number of new cases and deaths in the UAE, Saudi Arabia, and Kuwait. Test results based on out-of-sample forecast show that the proposed model achieves a high level of accuracy that is superior to many existing methods. Concretely, our model achieves mean absolute percentage error (MAPE) of 0.35%, 2.03%, and 3.75% in predicting the number of daily new cases for the three countries, respectively. Furthermore, interpolating our predictions to forecast the cumulative number of cases, we obtain MAPE of 0.0017%, 0.002%, and 0.024%, respectively. The strong performance of the proposed approach indicates that it could be a valuable tool in managing the pandemic.