Prediction error identification methods for stationary stochastic processes

The strong consistency of a general class of prediction error identification methods for stationary stochastic processes is demonstrated. In particular, the strong consistency of the maximum likelihood method for stationary Gaussian processes [4], [5] and of the quadratic loss prediction error method for stationary stochastic processes [1]-[3] follow as special cases of the general result.

[1]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[2]  K. Åström,et al.  Automatic Construction of Linear Stochastic Dynamic Models For Stationary Industrial Processes with Random Disturbances Using Operating Records , 1965 .

[3]  K. Åström,et al.  Numerical Identification of Linear Dynamic Systems from Normal Operating Records , 1966 .

[4]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .

[5]  W. Wonham.  On a Matrix Riccati Equation of Stochastic Control , 1968 .

[6]  J. Rissanen.  Recursive identification of linear systems , 1971 .

[7]  D. Mayne.  A canonical model for identification of multivariable linear systems , 1972 .

[8]  Peter E. Caines,et al.  Maximum likelihood estimation of parameters in multivariate Gaussian stochastic processes (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[9]  J. Rissanen.  Basis of invariants and canonical forms for linear dynamic systems , 1974, Autom..

[10]  M. Denham.  Canonical forms for the identification of multivariable linear systems , 1974 .

[11]  Peter E. Caines,et al.  Feedback between stationary stochastic processes , 1975 .

[12]  L. Ljung,et al.  Identifiability conditions for linear systems operating in closed loop , 1975 .

[13]  P. E. Caines,et al.  A Note on the Consistency of Maximum Likelihood Estimates for Finite Families of Stochastic Processes , 1975 .

[14]  L. Ljung,et al.  Estimation of Optimum Structures and Parameters for Linear Systems , 1976 .

[15]  L. Ljung.  On Consistency and Identifiability , 1976 .

[16]  Lennart Ljung,et al.  On The Consistency of Prediction Error Identification Methods , 1976 .