The principal objective is to assess the properties of a three-state hidden Markov model (HMM) over an 11,151-day historical gold price series. To find such a forecast, the gold price data are split into training and test samples, with the test subset containing current values for a 453-day period. Long short-term memory (LSTM), seasonal autoregressive integrated moving average (SARIMA), and gated recurrent units (GRUs) were the methods used to analyze the data. SARIMA, our reference model, handles the linear portion of time-series forecasts. The use of HMMs involves a wide range of topics, such as probability estimation, simulation using random number generators, estimation, and parametric characterization. LSTMs and GRUs are designed with a few internal gates to determine which of our time-series data is critical for keeping or discarding when solving short-term memory problems. The most important objective is to identify a high performer by utilizing performance metrics such as the root mean square error (RMSE) and mean absolute error (MAE). The outcomes were compared across methods using both quantitative and graphical presentations.

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