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This study aims to minimize the root mean square error for stock return by optimizing lags and hidden layers in a hybrid model. The model combines the autoregressive integrated moving average with the exogenous variables model as linear components. The residuals derived from linear components are used in artificial neural networks and Elman recurrent neural networks as non-linear components. A key feature of this approach is optimizing the selection of hidden layers and lags within the neural network, improving forecasting accuracy. The minimum mean square error forecast expression is derived, and the model is tested on stock price data during the COVID-19 period, marked by significant market shocks. The root mean square error results for the proposed model, traditional hybrid model, and traditional time series model range from 0.0004 to 0.01, 0.0006 to 0.01, and 0.006 to 0.03, respectively. The results show that the proposed model outperforms both traditional models.
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Sukchitt et al. (2025) studied this question.
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