The signals of microwave links used for wireless communications are prone to attenuation that can be significant due to rain. This attenuation may limit the capacity of the communication channel and cause irreversible damage. Accurate prediction of the attenuation opens the possibility to take appropriate actions to minimize such damage. In this paper, we present the use of the Long Short Time Memory (LSTM) machine learning method for short term prediction of the attenuation in commercial microwave links (CMLs), where only past measurements of the attenuation in a given link are used to predict future attenuation, with no side information. We demonstrate the operation of the proposed method on real-data signal level measurements of CMLs during rain events in Sweden. Moreover, this method is compared to a widely used statistical method for time series forecasting, the Auto-Regression Moving Average (ARIMA). The results show that learning patterns from previous attenuation values during rain events in a given CML are sufficient for generating accurate attenuation predictions.