## 4 Discussion
In the present study, there was a good fit because \(R^{2}\) values above 0.80 were obtained in all cases. Attaining low values for the MSE is important since the difference between a prediction and the actual value is expected to be close to zero. For the best NARX predictive models, the results were sufficiently successful with one hidden layer (MSE < 58.5) compared to ARIMAX (MSE \(\geq\) 95.6). For these NARX models, MAEs of between 5 and 13.5 were obtained, while for the ARIMAX models the values fluctuated between 7.7 and 11.8. It was observed that non-linear autoregressive models with or without exogenous inputs (NARX, NAR) are a successful and efficient tool to forecast export prices of Mexican lobster compared to ARIMAX models. This finding is based on the fact that the mean MSE of the 15 ANN models (73.07) was lower than the average of the four ARIMAX models (112.2); therefore, the neural networks provided better accuracy in the prediction of the real values, an aspect considered of great interest for application to fishery resources. Of note, these non-parametric models fit very well with price data that do not have a normal distribution [81]. Furthermore, it is important to use neural network models for long-term forecasting, since the commonly used ARIMAX models tend to decrease in accuracy over time [23]. The best prediction for the NARX model (with one exogenous variable) was obtained using the exogenous variable export volume of Mexican lobster to Hong Kong because it obtained the highest correlation value (0.86) and the lowest MSE (6.6). The information above was also corroborated using the other error measure (MAE), for which this variable also obtained the lowest value (MAE = 5) compared to the lowest MAE of the ARIMAX models (MAE = 7.7). Among the uncertainties of neural networks, it can be mentioned that they are sensitive to the scales of the variables and usually require a larger volume of data for model training. For large tasks, the more a network needs to learn, the more difficult it will be to teach. Increasing the number of patterns to identify or classify causes an increase in learning time, since the network invests more time in achieving convergence to the values of the weights with which the desired output is obtained. The results obtained with these models can be improved by using a larger number of data, i.e., historical series of daily data covering a longer period (preferably from several cooperatives). This approach would provide better ANN training and more accurate results in terms of fit and prediction. It is also suggested that the NARX model be improved using the results from applying an ARIMAX model to prices as an input variable. The present study shows that ANNs are suitable for predicting fishery resource prices. Information on future prices has several practical applications that have important implications for promoting the rational use of these resources. As mentioned above, pricing information facilitates the optimal allocation of effort throughout the season. In other cases, this information may also serve, to mention a few examples, to optimize inventory management (which is related to production costs) or as a tool for negotiating fairer contracts for both parties (by reducing information uncertainty and asymmetry) along the supply chain [82; 83]. From the governmental perspective, information on future prices is a useful element for designing management measures that promote sustainability, minimizing the economic losses of producers (e.g., [84]).