Sentiment Analysis is an innovative development technique that uses natural language processing techniques to derive people's emotions under positive, negative,and neutral based on public opinions of information. The main objective of this study is to introduce a novel stock market prediction method based on the Grey Exponential Smoothing method for analyzing social media data within a big-data distributed environment. The empirical investigation of this study is mainly carried out based on the stock market price indices parallel to the extracted Tweets collected during the three selected politically important moments that happened in Sri Lanka during the past ten years; the first case study is based on the political background after the ending of the thirty years of civil war in years 2009. In the year 2015,Maithripala Sirisena ended the dynastic rule of Mahinda Rajapaksa. So, the second case study has based the Tweets on the political reforms done after the 2015 presidential election; the third study is based on the Sri Lankan political and economic background after the Rajapaksas rose again in 2020. For validations purpose, K Nearest Neighbour, Decision Tree Model, Support Vector Machine, Grey Exponential Smoothing model, and Multinomial Naïve Bayes machine learning were considered. According to the empirical findings, the new proposed Hybrid Grey Exponential Smoothing model is highly accurate with the lowest RMSE error values in one-head forecasting. Furthermore, the key finding of this research suggested that the hybrid Grey Exponential Smoothing model performs well in sentiment classification-based financial predictions than traditional methods, especially with non-stationary behavioral backgrounds.