This study conducts a comparative analysis of two prominent methodologies, Time Series Analysis and Long Short-Term Memory Neural Networks (LSTM), for the prediction of stock prices, utilizing historical data from Netflix. The primary purpose of conducting this research is to evaluate their efficacy in terms of predictive accuracy. Time Series Analysis encompasses stationarity tests, rolling statistics, and the application of the Autoregressive Integrated Moving Average model. In contrast, LSTM Neural Networks involve data normalization, reshaping, and the development of LSTM-based models. Performance assessment metrics such as Mean Absolute Error, Mean Squared Error, Root Mean Squared Error, and visual comparisons are utilized. The results prominently favor long short-term memory Neural Network, which consistently outperforms in predictive accuracy, yielding reduced forecasting errors. This study contributes significant insights into stock price prediction methodologies and offers implications for refining model parameters, bolstering adaptability to evolving market dynamics, and addressing computational efficiency concerns in both Time Series Analysis and LSTM Neural Networks. In summary, LSTM model emerges as the preferred approach, advancing understanding of effective strategies for stock price prediction in financial markets.