## 5 Conclusions  
This study confirmed the predictive capacity of artificial neural networks (ANNs) to estimate the future export prices of Mexican lobster using exogenous variables associated with the market, particularly the demand for and supply of the fishery product.  
An important contribution of this work was the use of 31 exogenous variables associated with supply and demand. This is the first work where this approach is addressed, since the works that have been carried out in the past are more oriented to a fishery management approach (i.e., catch, fishing effort, closed areas, or exchange rate).  
The experimental results obtained with both models (NAR and NARX) showed that they fit the real data very well, with correlations greater than 86%.  
When autoregressive neural networks were applied with a single exogenous variable, a better prediction was obtained versus conventional autoregressive moving average models since the mean MSE value of the NARX models (43.2) was lower than that of the ARIMAX models (112.2). Additionally, the average MAE of these ANNs was lower (7.3) than that of the ARIMAX models (9.9).  
Another important contribution of the results shown by both models (NARX and ARIMAX) is that in terms of their adjustment they are similar (\(\bar{R}^{2}\) greater than 0.9); however, for forecasting, the ANNs show a better performance (with MSE and MAE values being lower for NARX).  
Another substantial finding of this work is that despite the fact that ARIMAX models have good accuracy over the short term and are often used, most of the neural models presented in this work were validated and showed a better accuracy; therefore, it is recommended to use these models for price forecasting fishery resources. The novelty of this work is that the models used can be replicated for lobster prices from other regions by properly selecting the exogenous variables that may impact the price.  
The price forecast values of Mexican red lobster obtained in this study are important for the market of this high-value product since this is the first time that these values have been estimated with artificial neural network models. Therefore, the present study demonstrates that ANNs are a useful tool for the price forecasting of fisheries resources, which could be extremely useful for red lobster fishing cooperatives, for those who manage the fisheries, and traders and investors who wish to obtain the greatest economic benefits.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app12126044/s1](https://www.mdpi.com/article/10.3390/app12126044/s1)]([https://www.mdpi.com/article/10.3390/app12126044/s1](https://www.mdpi.com/article/10.3390/app12126044/s1)), Table S1: Database containing date (month and year), real price, NARX and ARIMAX bestfit, export volume of Mexican lobster to China (VMExH), apparent national consumption (CNAMex), lobster production in Mexico (ProdMex) and export price of Australian lobsterworldwide (PAusMun); Table S2: Matrix of correlations between the 31 exogenous variables and the target variable.  
[PERSON] and [PERSON] developed the concept of applying neural networks in price forecasting for lobster. [PERSON] performed the mathematical analyses. [PERSON] contributed to the ARIMA analyses. [PERSON] and [PERSON] contributed with the discussion and conclusions. [PERSON] contributed to the bioeconomic analyses. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.