  We propose a novel method for variable selection in functional linear
concurrent regression. Our research is motivated by a fisheries footprint study
where the goal is to identify important time-varying socio-structural drivers
influencing patterns of seafood consumption, and hence fisheries footprint,
over time, as well as estimating their dynamic effects. We develop a variable
selection method in functional linear concurrent regression extending the
classically used scalar on scalar variable selection methods like LASSO, SCAD,
and MCP. We show in functional linear concurrent regression the variable
selection problem can be addressed as a group LASSO, and their natural
extension; group SCAD or a group MCP problem. Through simulations, we
illustrate our method, particularly with group SCAD or group MCP penalty, can
pick out the relevant variables with high accuracy and has minuscule false
positive and false negative rate even when data is observed sparsely, is
contaminated with noise and the error process is highly non-stationary. We also
demonstrate two real data applications of our method in studies of dietary
calcium absorption and fisheries footprint in the selection of influential
time-varying covariates.
