Deep learning techniques are making significant contributions to the rapid advancements in forecasting. A standout algorithm known for its ability to produce accurate forecasts by recognizing temporal autocorrelation within the data is the Long Short-Term Memory (LSTM) algorithm, a component of Recurrent Neural Networks (RNN). The LSTM method employs both stateless and stateful architecture approaches, providing versatility in its application. This research aims to compare stateful and stateless algorithms in LSTM models, focusing on forecasting stock prices, such as those of Apple Inc. This comparative analysis is crucial, taking into account various characteristics of time series data, including the benefits and drawbacks of temporal autocorrelation. The comparison results reveal that, despite the stateful algorithm requiring more computational time, it achieves greater accuracy than the stateless approach. The forecast indicates a potential upward trend in share prices for the period of January to December 2024, according to the projected outlook for Apple's stock value. However, it is essential to exercise prudence in interpreting these results, considering that share price fluctuations are influenced by a significant number of variables.