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This study aims to provide the best estimate of a stock's next day's closing price for a given day with the help of the hidden Markov model–Gaussian mixture model (HMM-GMM). The results were compared with Hassan and Nath’s (2005) study using HMM and artificial neural network (ANN).

The study adopted an initialization approach wherein the hidden states of the HMM are modelled as GMM using two different approaches. Training of the HMM-GMM model is carried out using two methods. The prediction was performed by taking the closest closing price (having a log-likelihood within the tolerance range) to that of the present one as the closing price for the next day. Mean absolute percentage error (MAPE) has been used to compare the proposed GMM-HMM model against the models of the research study (Hassan and Nath, 2005).

Comparing this study with Hassan and Nath (2005) reveals that the proposed model outperformed in 66 out of the 72 different test cases. The results affirm that the model can be used for more accurate time series prediction. Further, compared with the results of the ANN model from Hassan's study, the proposed HMM model outperformed 24 of the 36 test cases.

The study introduced a novel initialization and two training/prediction approaches for the HMM-GMM model. It is to be noted that the study has introduced a GMM-HMM-based closing price estimator for stock price prediction. The proposed method of forecasting the stock prices using GMM-HMM is explainable and has a solid statistical foundation.