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Abstract The foundation of Empirical dynamic modeling (EDM) is in representing time-series data as the trajectory of a dynamic system in a multidimensional state space rather than as a collection of traces of individual variables changing through time. Takens’s theorem provides a rigorous basis for adopting this state-space view of time-series data even from just a single time series, but there is considerable additional value to building out a state space with explicit covariates. Multivariate EDM case studies to-date, however, generally rely on building up understanding first from univariate to multivariate and use lag-coordinate embeddings for critical steps along the path of analysis. Here, we propose an alternative set of steps for multivariate EDM analysis when the traditional roadmap is not practicable. The general approach borrows ideas of random data projection from compressed sensing, but additional justification is described within the framework of Takens’s theorem. We then detail algorithms that implement this alternative method and validate through application to simulated model data. The model demonstrations are constructed to explicitly demonstrate the possibility for this approach to extend EDM application from time-series trajectories to effectively realizations of the underlying vector field, i.e. data sets that measure change over time with very short formal time series but are otherwise “big” in terms of number of variables and samples. 

Abstract Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated from available observations. Since observational data are frequently sampled with noise, it is possible that noise can corrupt the state-space representation degrading analytical performance. Here, we evaluate the synthesis of empirical mode decomposition with empirical dynamic modeling, which we term empirical mode modeling, to increase the information content of state-space representations in the presence of noise. Evaluation of a mathematical, and, an ecologically important geophysical application across three different state-space representations suggests that empirical mode modeling may be a useful technique for data-driven, model-free, state-space analysis in the presence of noise. 

Abstract The systematic substitution of direct observational data with synthesized data derived from models during the stock assessment process has emerged as a low-cost alternative to direct data collection efforts. What is not widely appreciated, however, is how the use of such synthesized data can overestimate predictive skill when forecasting recruitment is part of the assessment process. Using a global database of stock assessments, we show that Standard Fisheries Models (SFMs) can successfully predict synthesized data based on presumed stock-recruitment relationships, however, they are generally less skillful at predicting observational data that are either raw or minimally filtered (denoised without using explicit stock-recruitment models). Additionally, we find that an equation-free approach that does not presume a specific stock-recruitment relationship is better than SFMs at predicting synthesized data, and moreover it can also predict observational recruitment data very well. Thus, while synthesized datasets are cheaper in the short term, they carry costs that can limit their utility in predicting real world recruitment.