## 3 Results and Discussion
### Case of Parametric Analysis  
On the other hand, the parametric analysis was performed based on signal modeling using auto-regressive models. This method offers an approach from the predictive point of view using a specific mathematical model with a low number of parameters. Figure 6 shows the relationship between the number of delays (\(p\)) and the mean squared error (MSE)  
Figure 5: Decomposition of the electrical signal of _A. vera_ using the Wavelet Transform. obtained by fitting auto-regressive (AR) models of different orders. This analysis allowed identifying the optimal model order to capture the dynamics of the _A. vera_ electrical signal. The evaluation of the AR(9) model shows a mean squared error (MSE) of 17.86, with coefficients reflecting the decreasing influence of previous measurements over time. This model is computationally efficient and sufficiently accurate to represent the dynamics of the _A. vera_ electrical signal, meeting the objectives of the analysis. On the other hand, AR(15) obtained an MSE of 17.10, which is not a significant difference in terms of performance compared to AR(9) but is in terms of coefficients. This makes it more complex and computationally requires more resources. Based on the above, Equation (5) shows the obtained model from 9 delays (AR(9)),  
\[ \begin{split} x(n)&=34.2836+1.2137x(n-1)-0.0506x(n- 2)\\ &\quad-0.4592x(n-3)-0.0321x(n-4)\\ &\quad+0.2850x(n-5)-0.0722x(n-6)\\ &\quad-0.0886x(n-7)-0.0366x(n-8)\\ &\qquad\qquad+0.0715x(n-9),\end{split}  \tag{5}\]  
where \(x(n)\) represents the signal value at time \(n\), and the coefficients represent the weights of the lagged terms. The model parameters were estimated using the Yule-Walker method. The auto-regressive (AR) model implemented in Equation (4) was defined with an order of nine lags, selected as an advantage between prediction accuracy and model simplicity. Although higher orders (e.g., 15 lags) offered slight improvements in terms of mean squared error (MSE), the AR(9) manages to capture the main temporal dependencies with a significant reduction in the number of parameters. This model is similar and compares with the findings found by [PERSON], where they show an AR(18) [26]. Figure 7 shows the AR model predictions compared to the original signal measurements. It can be seen that the red line (AR) overlaps the blue line (original) almost completely. However, there are parts where the blue line is overlapped as in the abrupt change in the signal with signal reconstruction very similar to that previously reported in the literature [26]. The obtained model can be considered as simple and efficient from a computational resource usage point of view. This allows the generation of prediction tools in real time or for subsequent analysis with a larger volume of data. Although the AR model shows an acceptable prediction behavior, it is evident that non-parametric methods are better at capturing abrupt events. These results underline the relevance of combining the different approaches to obtain a complete overview of the electrical signal characteristics of _A. vera. Figure 6: MSE vs. \(p\) for AR model Selection. By highlighting this combination of approaches (non-parametric and parametric), Table 3 shows the performance metrics in the reconstruction and prediction of the electrical signal of the _A. vera_ plant from a non-parametric and parametric analysis approach. Both methods contribute to the analysis and modeling of the electrical signal of _A. vera_, but present differences in their application and results. On the one hand, the wavelet transform allowed the identification of transient events and abrupt changes in the signal. However, it requires an accurate selection of the mother function to achieve consistent results. In terms of computational cost, a higher capacity is required. On the other hand, the mathematical model obtained with the auto-regressive models presents a compact and efficient form for signal prediction. However, it does not fully capture the nature of the signal.