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We present a sparsity-promoting RBF algorithm for time-series prediction. We use a time-delayed embedding framework and model the function from the embedding space to predict the next point in the time series. We explore the standard benchmark data set generated by the Mackey–Glass chaotic dynamical system. We also consider a model of temperature telemetry associated with the mouse model immune response to infection. We see that significantly reduced models can be obtained by solving the penalized RBF fitting problem.