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Using multi-species time series data has long been of interest for estimating inter-specific interactions with vector autoregressive models (VAR) and state space VAR models (VARSS); these methods are also described in the ecological literature as multivariate autoregressive models (MAR, MARSS). To date, most studies have used these approaches on relatively small food webs where the total number of interactions to be estimated is relatively small. However, as the number of species or functional groups increases, the length of the time series must also increase to provide enough degrees of freedom with which to estimate the pairwise interactions. To address this issue, we use Bayesian methods to explore the potential benefits of using regularized priors, such as Laplace and regularized horseshoe, on estimating interspecific interactions with VAR and VARSS models. We first perform a large-scale simulation study, examining the performance of alternative priors across various levels of observation error. Results from these simulations show that for sparse matrices, the regularized horseshoe prior minimizes the bias and variance across all inter-specific interactions. We then apply the Bayesian VAR model with regularized priors to a output from a large marine food web model (37 species) from the west coast of the USA. Results from this analysis indicate that regularization improves predictive performance of the VAR model, while still identifying important inter-specific interactions.

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