# Forecasting Economy-Related Data Utilizing Weight-Constrained Recurrent Neural Networks
## 5 Conclusions  
In this work, we evaluated the classification accuracy of weight-constrained recurrent neural networks in forecasting economic data. The classification efficiency of these new prediction models was based on a recently-proposed training algorithm, which exploits the numerical efficiency and very low memory requirements of the limited memory BFGS matrices, together with a gradient-projection strategy for handling the bounds on the weights. By placing constraints on the values of weights, the likelihood that some weights will _\"blow up\"_ to unrealistic values is considerably reduced. Our numerical experiments demonstrated the classification efficiency of the proposed models, as confirmed statistically by the performance profiles. Therefore, we are able to conclude that the proposed algorithm appears to train RNNs efficiently with improved classification ability in domains such as forecasting economic benchmarks.  
The determination of optimal bounds on the weights is a rather challenging task; therefore, more research and experiments are needed. To this end, the question of what should be the values of the  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{\(F_{1}\)**-Score**} & \multicolumn{3}{c}{**Accuracy**} \\ \cline{2-7}  & **Bank** & **German** & **Banknote** & **Bank** & **German** & **Banknote** \\ \hline RNN (WCRNN1) & **0.93** & **0.77** & **0.98** & 91.64\% & 74.73\% & 97.88\% \\ RNN (WCRNN2) & **0.93** & **0.77** & **0.98** & **91.70\%** & **75.60\%** & 98.11\% \\ Naive Bayes & 0.88 & 0.72 & 0.79 & 86.76\% & 72.80\% & 79.66\% \\ SVM & 0.88 & 0.71 & 0.92 & 90.02\% & 73.60\% & 92.41\% \\
3 NN & 0.87 & 0.71 & 0.97 & 88.88\% & 72.40\% & 97.44\% \\ Random Forest & 0.91 & 0.74 & **0.98** & 91.30\% & 75.10\% & **98.32\%** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison of WCRNN1 and WCRNN2 against state-of-the-art classification algorithms, regarding \(F_{1}\)-score and accuracy.  
Figure 3: Log\({}_{10}\)-scaled performance profiles for the banknote authentication classification problem. The performance profile plots, for every \(\tau\geq 1\), the proportion \(P(\tau)\) of simulations for which any training algorithm has a performance within a factor \(\tau\) of the best algorithm. (**a**) \(F_{1}\)-score. (**b**) Accuracy.  
bounds for each benchmark or what constraints should be applied to the weights of each layer is still under consideration. An interesting idea could be to auto-adjust the bounds during the training process utilizing a strategy based on the use of a validation set. Probably, the required research to answer these questions, may reveal additional and crucial information and questions.  
Our future work is concentrated on incorporating the proposed methodology with more advanced and complex architectures such as long short-term memory neural networks and deep neural networks, together with sophisticated techniques such as dropout and batch normalization. Since our experimental results are quite encouraging, a next step could be the evaluation of the proposed framework for the prediction of stock exchange index movement and for forecasting the value of stock price indices and prices. Furthermore, another interesting aspect for future research could be the utilization of rule induction and discovery methods or even the use of synthetic data for further accuracy improvement based on the insights received in their training/testing periods (see [30; 31] and the references therein). Finally, we intend to conduct extensive empirical experiments by applying the proposed algorithm in specific scientific fields and to evaluate its performance on large real-world datasets, such as educational, healthcare, etc.  
This research received no external funding.  
The author declares no conflict of interest.