Acceleration of ab initio molecular dynamics (AIMD) simulations can be reliably achieved by extrapolation of electronic data from previous timesteps. Existing techniques utilize polynomial least-squares regression to fit previous steps' Fock or density matrix elements. In this work, the recursive Burg 'linear prediction' technique is shown to be a viable alternative to polynomial regression, and the extrapolation predicted Fock matrix elements were three orders of magnitude closer to converged elements. Accelerations of 1.8-3.4x were observed in test systems, and in all cases, linear prediction outperformed polynomial extrapolation. Importantly, these accelerations were achieved without reducing the MD integration timestep. (C) 2016 Elsevier B.V. All rights reserved.