Inflation forecasting has been and continues to be an important issue for the world's economies. Governments, through their central banks, watch closely inflation indicators to make national decisions and policies. This study proposes to forecast the inflation rate in five Latin American emerging economies based on the commonly used Seasonal Autoregressive Integrated Moving Average (SARIMA) approach combined with Long Short Term Memory (LSTM). Additionally, we run forecasts based on Fuzzy Inference Systems (FIS), Artificial Neural Networks (ANN), Artificial Neuro FIS, and SARIMA ANN as benchmarks to compare the performance of the combines SARIMA-LSTM. The Combined SARIMA-LSTM captures the linear aspects of the time series as well as the nonlinear aspects. The results indicate that the proposed model based on the combination of SARIMA and LSTM, have a higher accuracy in inflation forecasts with the proposed models over the SARIMA model and LSTM alone.