Time Series Models in Fish Recruitment - a Journey from Classical Statistics to Dynamic Models and Bayesian Forecasting

C.M. O'Brien CEF AS Lowestoft Laboratory Pakefield Road, Lowestoft Suffolk NR33 ORT United Kingdom fax: +441502513865 e-mail: [email protected] The investigation of stock-recruitment (S-R) relationships can result in functional models that are appealing when depicted in 2-dimensions as the level of recruitment versus spawning stock biomass. Translation of a functional S-R model to the third dimension of time may produce an estimated sequence of recruitment that bears little resemblance to the time series of recruitment used to estimate the 2-dimensional functional S-R model. This difference may result from mis-specification of modelling assumptions that may not have taken due account of temporal effects. By considering recruitment data for plaice (Pleuronectes platessa L.) in the North Sea, an autoregressive moving average (ARMA) model is developed to represent the recruitment process. The classical time series ARMA models can be reformulated as dynamic linear models (DLMs) which allow the incorporation of prior beliefs and expert information. The connection between the classical and Bayesian models is explored and the fundamental principles used by a Bayesian forecaster in structuring forecasting problems through dynamic models are briefly discussed.