GARCH-LSTM architectures.

Heteroscedasticity effects are useful for forecasting future stock return volatility. Stock volatility forecasting provides business insight into the stock market, making it valuable information for investors and traders. Predicting stock volatility is a crucial task and challenging. This study proposes a hybrid model that predicts future stock volatility values by considering the heteroscedasticity element of the stock price. The proposed model is a combination of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and a well-known Recurrent Neural Network (RNN) algorithm Long Short-Term Memory (LSTM). This proposed model is referred to as GARCH-LSTM model. The proposed model is expected to improve prediction accuracy by considering heteroscedasticity elements. First, the GARCH model is employed to estimate the model parameters. After that, the ARCH effect test is used to test the residuals obtained from the model. Any untrained heteroscedasticity element must be found using this step. The hypothesis of the ARCH test yielded a p-value less than 0.05 indicating there is valuable information remaining in the residual, known as heteroscedasticity element. Next, the dataset with heteroscedasticity is then modelled using an LSTM-based RNN algorithm. Experimental results revealed that hybrid GARCH-LSTM had the lowest MAE (7.961), RMSE (10.466), MAPE (0.516) and HMAE (0.005) values compared with a single LSTM. The accuracy of forecasting was also significantly improved by 15% and 13% with hybrid GARCH-LSTM in comparison to single LSTMs. Furthermore, the results reveal that hybrid GARCH-LSTM fully exploits the heteroscedasticity element, which is not captured by the GARCH model estimation, outperforming GARCH models on their own. This finding from this study confirmed that hybrid GARCH-LSTM models are effective forecasting tools for predicting stock price movements. In addition, the proposed model can assist investors in making informed decisions regarding stock prices since it is capable of closely predicting and imitating the observed pattern and trend of KLSE stock prices.

异方差性（Heteroscedasticity）效应对于预测未来股票收益波动率具有重要应用价值。股票波动率预测可为股票市场运作提供商业洞察，是投资者与交易者的宝贵参考信息。股票波动率预测是一项兼具关键性与挑战性的任务。本研究提出一种混合模型，通过考虑股票价格的异方差性元素来预测未来股票波动率数值。所提模型结合了广义自回归条件异方差模型（Generalized Autoregressive Conditional Heteroskedasticity，GARCH）与经典循环神经网络（Recurrent Neural Network，RNN）算法中的长短期记忆网络（Long Short-Term Memory，LSTM），该模型被命名为GARCH-LSTM模型。预期所提模型可通过纳入异方差性元素提升预测精度。首先，采用GARCH模型估计模型参数；随后，使用ARCH效应检验对模型所得残差进行检验，此步骤用于识别未被捕获的异方差性元素。ARCH检验的原假设若得到p值小于0.05的结果，则表明残差中仍包含有效信息，即异方差性元素。接下来，基于包含异方差性的数据集，采用基于LSTM的RNN算法进行建模。实验结果显示，相较于单一LSTM模型，混合GARCH-LSTM模型的平均绝对误差（MAE，7.961）、均方根误差（RMSE，10.466）、平均绝对百分比误差（MAPE，0.516）以及HMAE（0.005）均为最低。与单一LSTM模型相比，混合GARCH-LSTM模型的预测精度分别显著提升了15%与13%。此外，实验结果表明，混合GARCH-LSTM模型可充分利用GARCH模型估计未捕获的异方差性元素，其性能优于单一GARCH模型。本研究证实，混合GARCH-LSTM模型是预测股票价格走势的有效工具。此外，由于该模型能够精准拟合并复刻吉隆坡证券交易所（KLSE）股票价格的观测模式与趋势，因此可辅助投资者做出更明智的股票投资决策。