## 4 Results and Discussion
### Comparison with Other State-of-the-Art Models  
For issues involving time series prediction, RNNs are the most preferred models. In the field of natural language processing, they have performed particularly well. RNNs are all-purpose approximators, such as ANNs. Contrary to ANNs, recurrent cell feedback loops naturally handle the temporal dependencies and temporal order of the sequences [64]. In [65], the authors proposed an RNN model to forecast intermittent and lumpy time series data. To compare our model with the RNN model, results of lumpy data from [66] are considered here. An R package 'tsintermittent library' is used for the simulation process. A two-layer RNN model is used, which consists of 64 recurrent layers and a single node dense layer. Sigmoid and rectified linear unit (ReLu) are used as activation functions. A mean absolute error (MAE) is used for performance evaluation. The lower the MAE score, the better. This is because MAE is a measure of the average error between the predictions and intended targets; thus, we want to minimize this value. The results shows that RNN performs well in forecasting tasks, and the calculated MAE value is 0.6 as compared to the simple ANN model, where the calculated MAE value is 0.4. Comparison of the RNN model with ANN, Croston, and ANN-based approach using the Levenberg-Marquardt training algorithm, SVM, adaptive univariate SVM [39] and single exponential smoothing (SES) models was also carried out. The results show that the proposed approach based on gradient descent with momentum term outperforms the other methods in the case of lumpy data. MAE values obtained for different methods are listed in Table 5. A lower MAE indicates a better performance and vice versa. In [67], a comparison is made between various approaches to forecasting time series, including classical, machine learning, and deep learning approaches. This study examined four distinct classes of data, labeled A, B, C, and D. These classes are distinguished from one another according to the degree of lumpiness and intermittency exhibited by the data. Class C data are lumpy, and their characteristics are very comparable to those of the data we use in our work. Therefore, we will compare the results of our predictions with the forecasting results obtained from data C using various models. The research study that was referenced selected Croston, Holt-Winter, and Auto-ARIMA techniques from the classical methods category; RF, XGBoost, and Auto-SVR models from the machine learning category; and MLP and LSTM models from the deep learning category for evaluation and comparison. The LSTM displays the best performance with values of 0.97 for MASE, followed by Auto-ARIMA with values of 1.04 for MASE. The Croston technique has the worst performance, and its MASE value is greater than 2. MLP performs second worst with a value of 1.68, listed in Table 6. We also included several more approaches based on ANN with the traditional Levenberg-Marquardt algorithm, SVM and adaptive univariate SVM, and the results indicate improved performance of the proposed method vs. existing approaches. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & & \multicolumn{5}{c}{**Forecasted Dataset Values**} \\ \hline
**Quarters** & **1** & **2** & **3** & **4** & \\ \hline Normalized & 0.497869174 & 0.752308738 & 0.497869174 & 0.427485871 & **Forecasted** \\ \hline Descaled & 1.790411283 & 2.93538932 & 1.790411283 & 1.473686419 & 7.989898306 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Forecasted set of values. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \multirow{2}{*}{**Metric**} & \multirow{2}{*}{**RNN**} & \multirow{2}{*}{**Simple ANN**} & \multirow{2}{*}{**Croston**} & \multirow{2}{*}{**SES**} & \multicolumn{2}{c}{**ANN with Levenberg-Marquardt Training**} & \multirow{2}{*}{**SVM**} & \multicolumn{2}{c}{**Adaptive**} \\  & & & & & & **Algorithm** & & **SVM**[39] & **Proposed** \\ \hline MAE & 0.6 & 0.4 & 0.7 & 0.9 & 0.36 & 0.52 & 0.43 & 0.11 \\ \hline \hline \end{tabular}
\end{table}