The presence of complex, nonlinear dynamics in fish populations, and uncertainty in the structure (functional form) of those dynamics, pose challenges to the accuracy of forecasts produced by traditional stock assessment models. We describe two nonlinear forecasting models that test for the hallmarks of complex behavior, avoid problems of structural uncertainty, and produce good forecasts of catch-per-unit-effort (CPUE) time series in both standardized and nominal (unprocessed) form. We analyze a spatially extensive, 40-year-long data set of annual CPUE time series of North Pacific albacore (Thunnus alalunga) from 1° × 1° cells from the eastern North Pacific Ocean. The use of spatially structured data in compositing techniques improves out-of-sample forecasts of CPUE and overcomes difficulties commonly encountered when using short, incomplete time series. These CPUE series display low-dimensional, nonlinear structure and significant predictability. Such characteristics have important implications for industry efficiency in terms of future planning and can inform formal stock assessments used for the management of fisheries.