Singular spectrum analysis and autoregressive models for Ecuadorian shrimp catch forecasting

Abstract

Shrimp trawl fishing is a relevant activity that contributes significantly to the generation of economic resources for Ecuador through the creation of jobs and the commercialization of the shrimps. Unfortunately the high variability of the marine ecosystem signals are complex making forecasting a difficult task. This paper evaluates the use of singular spectrum analysis (SSA) for improving forecasting by conventional methods. SSA is implemented in four steps, embedding, decomposition, grouping, and diagonal averaging. The effective length of the embedding window is selected by means of the information provided by the differential energy of the eigenvalues. The SSA decomposition is used to extract two types of components, one of low frequency which represents the inter-annual component, and the other of high frequency which represents the annual component. Once the components have been obtained, three models based on SSA are implemented, the first is based on the autoregressive model (SSA-AR), the second is an artificial neural network (ANN) based on the Levenberg-Marquardt algorithm (SSA-ANN-LM), and the third is another ANN based on the Cuckoo Search algorithm (SSA-ANN-CS). The historical data that was used to evaluate the models are the shrimp monthly catches in the Gulf of Guayaquil from 2000 to 2012. The empirical results show the superiority of the proposed models with respect to the conventional models. The best approximation was achieved with the enhanced model SSA-AR, with a MAPE of 1.0%, a R 2 of 99% and a RMSE of 1.5%.