When considering time-series forecasting, the application of autoregressive models is a popular and simple technique that is usually considered. In this chapter, we present the basic theoretical aspects and assumptions of the ARIMA—Autoregressive Integrated Moving Average model. It is considered for the prediction of the COVID-19 epidemiological data series of five different countries (China, United States, Brazil, Italy, and Singapore), each of them with specific curves, which are results of the virus reproduction itself but also of policies and government decisions during the pandemic spread. The discussion about the results is performed with the focus on the three evaluation criteria of the model: R2 Score, MAE, and MSE. Higher R2 Score was obtained when the sample time series was smoothly increasing or decreasing. The error metrics were higher when the prediction was performed for oscillating data series. This may indicate that the use of ARIMA models may be suitable as a prediction tool for the COVID-19 when the country is not facing severe oscillations in the number of infections.