# Hybrid Crow Search Algorithm-LSTM System for Enhanced Stock Price Forecasting
## 4 Results
### Comparisons with Different Models  
This subsection compares the performances of the proposed system with those of typically applied neural-network models to time-series data, including RNN (recurrent neural networks) [55], gated recurrent unit (GRU) [56], LSTM (long short-term memory), and the VMD-LSTM proposed by [PERSON] et al. [57]. The time series contained data, including and excluding those from the COVID-19 period. The model comparisons are listed in Tables 6 and 7 (The bold numbers represent the best values) and in Figures 15 and 16 (in Figures 14 and 15, the testing set comprises approximately 20% of the entire datasets, which contain 2317 and 2158 points, respectively). Additionally, the term 'corr' was included in the names of the models that employed Pearson's correlation coefficient for feature extraction. Evidently, all standalone models (RNN, GRU, and LSTM) exhibited enhanced performance using Pearson's correlation coefficient for feature extraction, which proves that using this coefficient for feature extraction can enhance their performance. Furthermore, all models \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & 2330 & & & 0050 & & 2454 & \\ \hline  & RMSE & MSE & MAE & RMSE & MSE & MAE & RMSE & MSE & MAE \\ \hline
3 days & **6.382** & **40.724** & **4.755** & 1.182 & 1.397 & 0.871 & **11.095** & **122.297** & **7.989** \\ \hline
4 days & 7.601 & 57.778 & 5.607 & **1.177** & **1.386** & **0.872** & 12.593 & 158.581 & 8.827 \\ \hline
5 days & 9.765 & 95.362 & 7.64 & 1.243 & 1.545 & 0.923 & 13.915 & 193.629 & 9.764 \\ \hline
7 days & 9.433 & 88.983 & 7.404 & 1.285 & 1.651 & 0.954 & 14.015 & 196.43 & 9.765 \\ \hline
10 days & 12.462 & 155.293 & 9.781 & 1.468 & 2.156 & 1.146 & 13.86 & 192.113 & 10.316 \\ \hline
30 days & 16.424 & 269.735 & 14.264 & 1.835 & 3.366 & 1.556 & 12.459 & 155.228 & 9.358 \\ \hline  & & 1216 & & & 2882 & & & Time Step performance \\ \hline  & RMSE & MSE & MAE & RMSE & MSE & MAE & RMSE & MSE & MAE \\ \hline
3 days & **0.664** & **0.441** & **0.511** & 0.362 & 0.131 & 0.272 & **3.937** & **32.998** & **2.879** \\ \hline
4 days & 0.819 & 0.671 & 0.611 & 0.422 & 0.178 & 0.306 & 4.522 & 43.718 & 3.244 \\ \hline
5 days & 0.796 & 0.634 & 0.632 & 0.395 & 0.156 & 0.293 & 5.222 & 58.265 & 3.844 \\ \hline
7 days & 0.761 & 0.579 & 0.581 & 0.395 & 0.156 & 0.293 & 5.177 & 57.559 & 3.799 \\ \hline
10 days & 0.743 & 0.552 & 0.574 & 0.372 & 0.139 & 0.274 & 5.781 & 70.050 & 4.418 \\ \hline
30 days & 0.674 & 0.454 & 0.521 & **0.331** & **0.109** & **0.245** & 6.344 & 85.778 & 5.188 \\ \hline \end{tabular}
\end{table} 
Table 5: Result of time step. performed better on data, excluding the COVID-19 period, possibly due to significant price fluctuations during this period. We speculate that this may be due to the heightened market volatility and uncertainty during the pandemic, which led to sudden and unpredictable fluctuations in stock prices. These unusual market conditions could have made it more difficult for the model to accurately predict price movements, as the model might not have been trained to handle such extreme deviations from typical market patterns. Finally, the proposed model demonstrated superior average performance compared to all other models. As a result, we conclude that it provides more accurate predictions than the RNN, GRU, LSTM, and VMD-LSTM.