Fish are organisms that cannot regulate the temperature of the environment independently, and the environment temperature changes influence their geographical distribution, migratory routes, and occupation of habitat [1
]. On the other hand, although the species present variability associated with environmental changes, the composition and abundance are also affected by predators, competitors, and prey [2
]. The link between the variation of anchovy abundance and environmental changes in different time-space scales opens the possibility of predicting fluctuations in landings in the short, medium, and long term [3
]; which is one of the main objectives of fisheries’ management [4
As indicated by [5
], it is fundamental to consider the impact of the environment and the interactions between fisheries for their management. In effect, the fisheries show different trends in response to environmental changes, since these changes affect various stages of larvae, reproduction, grazing habitat, and migration of different populations. In addition, an inevitable increase in fishing effort must be added. Potential climate change and climate variability at different time scales have immediate or phase effects, both locally and regionally. Possible changes in environmental variables such as sea surface temperature (SST), depth of the mixing layer, depth of the thermocline, intensities of up-welling currents, the mechanism of nutrient concentration, and changes in the ice marine layers [2
], although mild, may affect the food chain, thus drastically altering the abundance, distribution, and availability of fish populations. In addition, climatic change could have consequences on the composition of the community and the performance of ecosystems [6
Regarding the environment and resource analysis in the anchovy and sardine fisheries of northern Chile, the work in [7
] developed an artificial neural network (ANN) model for the anchovies’ fishery. In [8
], the authors developed a multivariate ANN model considering monthly environmental variables such as the sea surface temperature, up-welling index, and sea level; while [9
] developed ANN models for anchovy and sardine, respectively, taking into account, in addition to the environmental variables, the interaction between species. These studies made a brief analysis of the correlation between variables, self-correlation, and cross-correlation using non-linear functions to find functional relationships to introduce different models [2
]. On the other hand, the wok in [10
] predicted the environmental variability in the anchovy fishery in the northern zone of Chile, through the development of spatio-temporal indicators of the ecosystem, statistical relationships between indicators, GIS functions (Geographical Information Systems), and ANN models, offering an integration in the prediction of anchovy abundance.
With respect to other statistical techniques implemented to forecast fishing landings, there was the application of a hybrid model studied by [11
], in which the potentialities of autoregressive models integrated moving averages (ARIMA) were combined with wavelet theory to enhance the precision of fishing landings’ forecasts in Malaysia. Their study found that the combined model provided more accurate forecasts of fishing landing series than the individual ARIMA model. Other studies have presented a forecast strategy based on the decomposition of stationary wavelets combined with linear regression to improve the accuracy of pelagic one month ahead fish catches predictions of the fishing industry in the southern zone of Chile [12
]. The authors demonstrated the usefulness of the strategy in the anchovy catch dataset for monthly periods, explaining
of the variance with a parsimonious reduction.
Considering the above and in virtue of the fact that in Chile, the average annual landings in the last 30 years was 4.8 million tons and the agricultural resources in the northern zone represent
], as well as given that in this area, the fishery is based successively on anchoveta (Engraulis ringens
) and sardine (Sardinops sagax
), with notable changes associated with fishing effort and environmental fluctuations (see [14
]), it is considered pertinent to implement scientific techniques aimed at studying functional relationships that can be analyzed in depth, in order to reduce gaps in the implementation of national fisheries’ management policies and provide the basic knowledge that supports the making of such decisions [2
Currently, the correct prediction of fishing landings in particular is a point of special interest for fisheries’ management, and researchers who focus on modeling time series of landings are looking for prediction models that take into account various patterns. In the literature, most researchers implement potential methods such as ANN and hybrid models such as autoregressive integrated mobile average with ANN, among others, effectively synced to model time series and predict fishing landings; however, there is still a wide range of hybrid techniques that can be implemented to achieve improvements in predictions.
In this sense, this research proposes the implementation of highly predictive techniques to model and study climatic phenomena, specifically the quantitative characterization of the elements that determine the monthly disembarkation of anchovies and sardines in northern Chile. The work revolves around the following question: Which time series model would allow forecasting more accurately the monthly disembarkation of anchovies and sardines registered in northern Chile, under the influence of macro-climatic variables such as the sea surface temperature and the associated ENSO phenomenon?
The benefits of our research reside in the improvements obtained in the adjustment and forecasting of anchovy landings when the series are broken down into their high and low frequency components, by expanding the transfer function coefficients to a time varying approach by using a least squares procedure. It also highlights the improved performance of using the combination of traditional statistical techniques with the aforementioned extension when implemented to forecast sardine landings. Likewise, seeking to optimize the goodness of fit and quality of the forecast, it was also observed that after the application of various transformations to stabilize the variability of the observed series, significant improvements in the results could be achieved.
The paper is divided as follows: In Section 2
, we briefly describe the time series modeling strategy and the required steps to fit these models. In Section 3
, we explain the datasets used in the analysis, the methodology to process them, and all the results at each step, when fitting the transfer function models. We finally provide in Section 4
some conclusions and potential extensions of this work.
Based on the analysis of models built to forecast the monthly disembarkation of anchovy (Engraulis ringens) and sardine (Sardinops sagax) in northern Chile, the following conclusions emerged from the analysis:
When various transformations were applied to the data to achieve better model precision, large differences in the benefits of the selected fitted models could be identified. Records of anchovy landings were better fitted and forecast with standardized data under a transfer model with wavelet coefficients, using Daubechies 10 filters with low resolution levels (associated with the slightly compressed wavelets ). Sardine landings were better fitted when the variance of the landings was stabilized using the logarithmic function; and the variance of the explanatory variables was stabilized by anomalizing the variables; finally, modeling these sardine landings in a logarithmic scale with a traditional transfer function.
The variables that allowed explaining in a more robust way the disembarkation of anchovy was the turbulence index from Antofagasta Coastal Oceanographic Station (TI) and the Pacific sea surface temperature index (Niño Zone 1 + 2: N12); while the disembarkation of sardines was explained by local climatic variables: TI, sea surface temperature from Antofagasta Coastal Oceanographic Station (SST), and the log disembarkation of anchovy.
Given that the process of selecting the appropriate number of scales to optimize the model fit was made according to the researcher’s choice, it is advisable to implement in the future some entropy based techniques that allow for the best possible scale selection. It is also recommended to evaluate if the results can be optimized considering other wavelet filters in addition to the Daubechies filters. Likewise, a non-linear structure model could be considered (for example, thresholding wavelet coefficients) in order to determine the best model structure for fishery prediction. These results could also be optimized by implementing bootstrapping techniques for the fitted parameters in order to quantify their uncertainty.