The application of a general time series model to floodplain fisheries in the Amazon

• A model to capture the main patterns of a fisheries system in the Amazon is proposed.
• Fishery yield time series were considered as a multivariate response.
• An additive multivariate (VAR) model with exogeneous and cyclical variables was fitted.
• The model explained, on average, 78% of the variability in yield of the study species.

Time series analysis is a common tool in environmental and ecological studies to construct models to explain and forecast serially correlated data. There are several statistical techniques that are used to deal with univariate and multivariate (more than one series) chronological patterns of fisheries data. In this paper, an additive stochastic model is proposed with explicative and predictive features to capture the main seasonal patterns and trends of a fisheries system in the Amazon. The model is constructed on the assumption that the multivariate response variable – vector containing fishery yield of eight periodic species and the total fishery yield – can be decomposed into three terms: an autoregression of the response vector, an exogenous environmental variable (river level), and a seasonal component (significant frequencies obtained by using spectral analysis and the periodogram indicating the regularity of periodic cycles in the natural and fisheries system). The estimation procedure is carried out via maximum likelihood estimation. The model explained, on average, 78% of the variability in yield of the study species. The model represents the optimal solution (minimum mean square mean error) among the class of all multivariate autoregressive processes with exogenous and seasonal variables. Predictions for one period ahead are provided to illustrate how the model works in practice.