The contemporary financial landscape is characterized by dynamic market behavior. Accurate predictions of stock price movements are not only of paramount importance for financial decision-makers but also pose a significant challenge due to the inherent complexities of financial markets. This research study delves into the realm of stock market prediction by employing a comprehensive approach that combines time series analysis and machine learning techniques. The main goal is to assess different models in predicting price trends, potentially reshaping stock market forecasts and emphasizing the need for tailored predictive approaches for individual stocks. The study focuses on the example of Apple Inc. (AAPL) stock data and aims to uncover the effectiveness of various models in forecasting its price trends. Our results emphasize that the LSTM model surpasses the conventional ARIMA model in terms of forecasting accuracy, suggesting a promising path for improving stock market predictions. This comparative exploration provides insights into the potential of machine learning models in refining stock market predictions and highlights the importance of tailoring predictive methodologies to individual stock behaviors.