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In economics, business and technology, predictive analysis of the time series data is an essential aspect. Traditionally, so many methods exist to efficiently predict the next lag of time series data. The main aim of the research is to investigate the functionality of the stock exchange in the improvement of the Indian economy utilizing the time series data of various industrial sectors from the years 2000 to 2020 and to conduct the comparative time series analysis of machine learning models like ARIMA, ARIMAX and recurrent neural network model like LSTM. The results of the research show that ARIMAX model has outperformed the ARIMA and LSTM models. Also, from this analysis, it can be understood that the performance of the LSTM model is better for the larger datasets. In addition, it was observed that increasing the number of epochs does not impact the performance of the LSTM model and showed a purely random behavior. The addition of exogenous features to the Auto ARIMA model is commonly called as ARIMAX model. This addition of exogenous features like date time features to the stock price data improvises the performance of the ARIMAX model.