Over the last few years, incremental machine learning for streaming data has gained significant attention due to the need to learn from a constantly evolving stream of data without the need to store it. The advent of big data has further fuelled research on developing systems that can cope with continuously changing data streams and tackle the challenges associated with historical data requirements. The problem of time series forecasting has been studied using varied approaches like neural networks, ensemble methods, decision trees and rules, support vector machines to name a few. However, neural network models have gained particular attention in dealing with changing data distribution due to their generalization abilities. In this paper, we propose a prequential framework named PS-PGSM which involves incrementally training the base models and online Regions of Competence (ROC) computation followed by selection of the best forecaster for the task of time series forecasting using saliency maps. We build upon the state-of-the-art approach named OS-PGSM (Online Model Selection using Performance Gradient based Saliency Maps) in which the model training and ROC computation is performed offline. Past research has demonstrated that a set of different models enables specialization for each model compared to a single forecasting model which is particularly useful when predicting for an evolving time series sequence. Our approach uses saliency maps for prequential calculation of ROC for each model to find the best forecaster based on the performance of each model. We evaluate the proposed approach against OS-PGSM, as well as against previous best performing model by first conducting preliminary experiments on 10 real-world time series datasets and then using 2 real-world big datasets to showcase its applicability to big data. Experimental results not only validate the effectiveness of our approach for big data but also demonstrate superior performance in terms of prediction accuracy and computational time efficiency while also handling concept drift.