In this study, the forecasting capabilities of nonlinear models as Artificial Neural Networks and linear ARIMA models were compared. The comparison was conducted using the daily data of Nigeria’s All Share Index for 11 years. The empirical findings revealed ARIMA (1,1,2) model as the best fit for Nigeria’s All Share Index among other Box Jenkins models. This was supported by the most fit statistic test. Also, ANN model with three units in the hidden layer, two lags and the learning rate equal to 0.1, returned as the best fit for the Nigeria All Share Index forecasting. Furthermore, while comparing the performance of the two models, the RMSE of the ARIMA model equivalent to 0.0136 is higher than the RMSE of the ANN model (0.0048), indicating the efficiency of the ANN model. Thus, we can conclude from the above statistics that the ANN model is more efficient. As a result, the study recommends taking advantage of the high capacity of artificial neural networks as a forecasting technique in other fields, such as medical research, genetics research, industrial research, energy, and military research.