In this research, an algorithm is presented for predicting the remaining useful life (RUL) of aircraft engines from a set of predictor variables measured by several sensors located in the engine. RUL prediction is essential for the safety of those aboard, but also to reduce engine maintenance and repair costs. The algorithm combines time series analysis methods to forecast the values of the predictor variables with machine learning techniques to predict RUL from those variables. First, an auto-regressive integrated moving average (ARIMA) model is used to estimate the values of the predictor variables in advance. Then, we use the result of the previous step as the input of a support vector regression model (SVM), where RUL is the response variable. The validity of the method was checked on an extensive public database, and the results compared with those obtained using a vector auto-regressive moving average (VARMA) model. Our algorithm showed a high prediction capability, far greater than that provided by the VARMA model.