## 3 Results
### Berry Time Series Results  
This section unveils the compelling results obtained from analyzing three weekly berry production series during the 2020-2021 season.  
To predict weekly strawberry yields, both the NAR network and NAR-SVR network employed the sigmoidal activation function in the hidden layer. The NAR model utilized 13 inputs in the input layer and 6 nodes in the hidden layer. Backpropagation algorithm with a learning coefficient of \(\eta=0.1\) facilitated the training process. Meanwhile, the NAR-SVR model employed an SVR model with 4 inputs, utilizing the Gaussian function as the kernel. Utilizing the e1071 package, the parameter values were computed, resulting in the following outcomes: \(C=1\), \(\gamma=1\), and \(\epsilon=0.1\).  
In the case of weekly raspberry predictions, both networks utilized 2 inputs and 20 nodes in the hidden layer. The sigmoidal function served as the activation function. To ensure smooth convergence, a lower learning rate of \(\eta=0.01\) was employed with the backpropagation algorithm. Furthermore, the SVR model used 4 inputs, the Gaussian function with \(\gamma=0.25\), and constant values of \(\epsilon=0.1\) and \(C=1\) for error correction.  
For the two blueberry neural networks, the hidden layer incorporated 10 inputs and 7 nodes. Both the NAR and NAR-SVR networks utilized the sigmoid activation function with a learning constant of \(\eta=0.1\) for the backpropagation technique. In the NAR-SVR model, the error-correcting ML component employed 8 inputs and a Gaussian activation function with \(\gamma=0.125\), \(\epsilon=0.1\), and \(C=1\).  
Table 1 displays the results of both neural network types in comparison with AR(1), ARIMA(1,1,1), and SVR models, utilizing input numbers of 3, 4, and 10, along with the Gaussian activation function on the primary variable.  
In terms of accuracy, the NAR-SVR network exhibited superior performance, particularly in the strawberry and raspberry datasets, while maintaining satisfactory results for blueberries. Notably, the NAR-SVR method outperformed the ARIMA and SVR models, underscoring its efficacy in capturing the underlying patterns and enhancing predictive capabilities.  
The comparative graphs of the models with respect to the observed variables of strawberries, raspberries, and blueberries are depicted in Figure 2. Notably, the NAR-SVR model exhibits a significantly better fit compared to the NAR model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Strawberry Model** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** \\ \hline NAR & 0.875 & 108,818.00 & 218,035.20 \\ NAR-SVR & 0.897 & 96,192.39 & 198,001.30 \\ AR(1) & 0.805 & 112,350.30 & 272,086.80 \\ ARIMA(1,1,1) & 0.886 & 101,767.80 & 208,013.20 \\ SVR & 0.795 & 149,745.00 & 279,310.80 \\ \hline
**Raspberry Model** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** \\ \hline NAR & 0.898 & 3963.26 & 6820.32 \\ NAR–SVR & 0.933 & 3094.87 & 5521.29 \\ AR(1) & 0.776 & 5667.00 & 10,132.67 \\ ARIMA(1,1,1) & 0.796 & 4204.36 & 9656.68 \\ SVR & 0.835 & 4663.82 & 8706.49 \\ \hline
**Blueberry Model** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** \\ \hline NAR & 0.906 & 18,736.12 & 28,500.04 \\ NAR–SVR & 0.916 & 17,985.56 & 26,919.89 \\ AR(1) & 0.609 & 30,773.63 & 58,217.35 \\ ARIMA(1,1,1) & 0.914 & 18,207.08 & 27,282.07 \\ SVR & 0.572 & 34,628.62 & 60,854.12 \\ \hline \end{tabular}
\end{table}
Table 1: Results for berry time series, 2020–2021.  
Figure 2: Prediction charts for berry time series, 2020–2021.