## 4 Experimental Results
### One-Time-Step Prediction Comparisons between Proposed and Benchmark Models  
In this subsection, we provide the experimental results of the proposed models to predict the one-time-step ahead of the three stock market indices. We evaluated the performance of the proposed models with various look-back periods of \(5,21\), and \(42\) days as one week, one month, and two months, respectively, for different periods. The proposed and benchmark models were implemented as described in previous sections. The Adam optimizer and OHLV features were used for all methods in Table 3.  
Table 3 compares our models and the benchmark models for the different look-back periods for one-time-step prediction, where the best performance results are marked in bold for each stock market index, period, and metric. According to the results in Table 3, increasing the look-back period slightly enhances the performance across all operating conditions by keeping all other hyperparameters constant. Moreover, a very long sequence length, such as the look-back period of \(42\), increases the performance. From \(1\) January \(2000\) through \(31\) December \(2019\), the proposed models improved the benchmarks in \(77.8\%\) and \(77.8\%\) of cases in terms of MSE and MAE, respectively. Additionally, our models outperformed the benchmarks in \(66.7\%\) and \(77.8\%\) of cases in terms of MSE and MAE, respectively, for the period from \(1\) January \(2017\) through \(31\) December \(2019\), before the COVID-19 pandemic, and in \(100\%\) of cases for the period from \(1\) January \(2019\) through \(31\) December \(2021\), after the COVID-19 pandemic, in terms  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Look-Back**} & \multirow{2}{*}{**Metric**} & \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**2009-2019 1**} & \multicolumn{3}{c}{**2017-2019 2019**} \\ \cline{3-11}  & & & **DAX** & **DOW** & **\&  
of both MSE and MAE. Some results were the same for different benchmarks because the training algorithm might find the local optima. Further, an overall comparison between the ensemble model and other models in Table 3 indicates that the ensemble model significantly outperformed the other models. We evaluated the performance of the proposed models with four different features (i.e., MV, MVC, OHLV, and OHLMVC) in addition to a novel feature, medium, defined as the average of high and low prices. In comparison, OHLVs have been commonly used as features in other studies. In addition, we evaluated the performance of our models using two different optimizers, Adam and RMSProp, by keeping all other hyperparameters constant. The average MSE and MAE over the three periods for the impact of different features and optimizers of the proposed models are shown in Tables 4 and 5, where the best performance results are marked in bold for each stock market index, a look-back period, and optimizer. Regarding the one-time-step prediction, Table 4 shows that the CNN-LSTM, GRU-CNN, and ensemble models with the novel medium feature outperformed the other models in 83.3%, 33.3%, and 0% of cases with the DAX dataset; 83.3%, 100%, and 16.7% of cases with the DOW dataset; and 83.3%, 83.3%, and 33.3% of cases with the S&P500 dataset, respectively, in terms of the average MSE over the three periods. Table 5 shows that the CNN-LSTM, GRU-CNN, and ensemble models incorporating the medium feature outperformed the other models in 83.3%, 33.3%, and 16.7% of cases with the DAX dataset; 83.3%, 100%, and 16.7% of cases with the DOW dataset; and 66.7%, 66.7%, and 33.3% of cases with the S&P500 dataset, respectively, in terms of the average MAE over the three periods. An overall comparison between the models incorporating the medium feature and the models without the medium feature shows that adding the medium feature improves the performances of all models.