This paper by Hirotugu Akaike introduces a practical procedure for predictor identification, focusing on the final prediction error (FPE) as a figure of merit. The FPE is defined as the mean square prediction error of a predictor. The procedure involves fitting autoregressive models of successive orders within a prescribed range, computing FPE estimates for each model, and selecting the one with the minimum FPE. The statistical characteristics of these FPE estimates and the overall procedure are discussed to demonstrate their practical utility. A modified version of the original procedure is proposed, which shows consistency in estimating the order of a finite-order autoregressive process. Additionally, the FPE is applied to determine the constants in a decision procedure proposed by T. W. Anderson for the order of a Gaussian autoregressive process. The performances of the three procedures—original, modified, and Anderson’s—are compared using various artificial time series, showing that the original procedure is most useful for practical applications where the true orders of autoregressive processes are generally infinite. The implications of this identification procedure on power spectrum estimation will be discussed in a subsequent paper. The paper also introduces the notation used for vectors and matrices and defines the FPE for a linear predictor of a stationary process.This paper by Hirotugu Akaike introduces a practical procedure for predictor identification, focusing on the final prediction error (FPE) as a figure of merit. The FPE is defined as the mean square prediction error of a predictor. The procedure involves fitting autoregressive models of successive orders within a prescribed range, computing FPE estimates for each model, and selecting the one with the minimum FPE. The statistical characteristics of these FPE estimates and the overall procedure are discussed to demonstrate their practical utility. A modified version of the original procedure is proposed, which shows consistency in estimating the order of a finite-order autoregressive process. Additionally, the FPE is applied to determine the constants in a decision procedure proposed by T. W. Anderson for the order of a Gaussian autoregressive process. The performances of the three procedures—original, modified, and Anderson’s—are compared using various artificial time series, showing that the original procedure is most useful for practical applications where the true orders of autoregressive processes are generally infinite. The implications of this identification procedure on power spectrum estimation will be discussed in a subsequent paper. The paper also introduces the notation used for vectors and matrices and defines the FPE for a linear predictor of a stationary process.