Landslides and associated slope movements are common occurrences in the hilly regions. In particular, Tangni in Uttarakhand state between Pipalkoti and Joshimath has experienced a number of landslides in the recent past. Prior research has used a certain moving average and machine-learning (ML) algorithms to predict slope movements. However, a comparison of these methods for real-world slope movements has been less explored. The primary objective of this paper was to compare a seasonal autoregressive integrated moving average (SARIMA) model, a multilayer perceptron (MLP) model, and a long short-term memory (LSTM) model to predict slope movements recorded at the Tangni landslide in Chamoli, India. Time series data about slope movements from five sensors placed on the Tangni landslide hill were collected daily over a 78-week period from July 2012 to July 2014. Different model parameters were calibrated to the training data (first 62 weeks) and then made to predict the test data (the last 16 weeks). Results revealed that the moving-average models (SARIMA) performed better compared to the ML models (MLP and LSTM) during both training and test. We highlight the implication of using moving-average models for predicting slope movements.