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If a noncausal two-dimensional (2-D) autoregressive (AR) process is bi-causal, there exists a causal 2-D AR process on the nonsymmetric half-plane having the same autocorrelations as the noncausal 2-D AR process. A formula is presented to relate the AR coefficients of the noncausal 2-D AR process with those of the causal 2-D AR process on the nonsymmetric half plane. The 2-D Yule-Walker equations are derived for causal 2-D AR models on the nonsymmetric half plane. A computationally efficient order-recursive algorithm is proposed to solve the 2-D Yule-Walker equations. Using the autocorrelation equivalence relation and the order-recursive algorithm, we can easily identify a noncausal 2-D AR process from its autocorrelations.