In this paper, we propose a speed prediction model using auto-regressive integrated moving average (ARIMA) and neural networks for estimating the futuristic speed of the nodes in mobile ad hoc networks (MANETs). The speed prediction promotes the route discovery process for the selection of moderate mobility nodes to provide reliable routing. The ARIMA is a time-series forecasting approach, which uses autocorrelations to predict the future speed of nodes. In the paper, the ARIMA model and recurrent neural network (RNN) trains the random waypoint mobility (RWM) dataset to forecast the mobility of the nodes. The proposed ARIMA model designs the prediction models through varying the delay terms and changing the numbers of hidden neuron in RNN. The Akaike information criterion (AIC), Bayesian information criterion (BIC), auto-correlation function (ACF), and partial auto-correlation function (PACF) parameters evaluate the predicted mobility dataset to estimate the model quality and reliability. The different scenarios of changing node speed evaluate the performance of prediction models. Performance results indicate that the ARIMA forecasted speed values almost match with the RWM observed speed values than RNN values. The graphs exhibit that the ARIMA predicted mobility values have lower error metrics such as mean square error (MSE), root MSE (RMSE), and mean absolute error (MAE) than RNN predictions. It yields higher futuristic speed prediction precision rate of 17% to 24% throughout the time series as compared with RNN. Further, the proposed model extensively compares with the existing works.