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Grover's equation [L.K. Grover, Local search and the local structure of some NP-complete problems, Operations Research Letters 12 (1992)] and, equivalently, the Laplacian equation [J.W. Barnes, S. Dokov, B. Dimova, A. Solomon, A theory of elementary landscapes, Applied Mathematics Letters 16 (2003)] define an elementary landscape which has favorable properties for direct search methods. Dimova et al. [B. Dimova, J.W. Barnes, E. Popova, Arbitrary elementary landscapes & AR(1) processes, Applied Mathematics Letters (in press)] prove that the autocorrelation function associated with an arbitrary elementary landscape is consistent with an AR(1) time series. In this work, we develop the characteristic landscape equation for AR(2) consistent landscapes and show that they also possess favorable properties for direct search methods.