EVALUATION OF AUTOREGRESSIVE MODEL BY INFORMATION AMOUNT AND APPLICATION TO NON-GAUSSIAN PROCESS.

Problems in the study of the autoregressive equations describing a stationary normal probabilistic process include determining equivalence of the system, prediction of the system and calculation of the power spectra. In conforming to the autoregressive model the order of the model has to be estimated. For estimation of the order of the model the maximum likelihood method and the final prediction error method, which is a modified maximum likelihood method, are available. In both of these methods the evaluation functions of conformation are formed with the mean square of the difference between the linear prediction formula and observed data, with certain coefficients. In this paper, first, by introducing the average information to the autoregressive equation the mean square of the prediction error is expressed as an equation of the autocorrelation determinant. This expression replaces the conventional procedure for calculation of the regression coefficients in terms of the least square method and is an evaluation formula for order estimation with a wide range of application. A data preprocessing scheme to express data of a non-normal process in terms of the autoregressive model is discussed. That is, by introducing the Kullback-Leibler information, it is shown that the information is invariant for a homeomorphic mapping which transforms a non-normal process to a normal process. Finally, the proposed preprocessing scheme is discussed from a statistical viewpoint by computer simulation.