ARMA model order determination and MDL: a new perspective

Much research has focused on the problem of estimating the model order of autoregressive moving average (ARMA) processes. The most well-known of the proposed solutions for this problem include the final prediction error (FPE), Akaike information criterion (AIC), and minimum description length (MDL). A new approach for model order determination based on the MDL criterion is proposed and shown to depend on the minimum eigenvalue of a covariance matrix derived from the observed data. As a result, a new selection procedure for estimating the model order via MDL is proposed. Examples that illustrate the significantly improved accuracy of the proposed technique are given.<<ETX>>

[1]  D. Mitchell Wilkes,et al.  Enhanced rational signal modeling , 1991, Signal Process..

[2]  James Durbin,et al.  The fitting of time series models , 1960 .

[3]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[4]  H. Akaike.  A new look at the statistical model identification , 1974 .

[5]  E. Hannan,et al.  The determination of optimum structures for the state space representation of multivariate stochastic processes , 1982 .

[6]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[7]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[8]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[9]  T. Söderström.  On model structure testing in system identification , 1977 .

[10]  J. Cadzow,et al.  Algebraic approach to system identification , 1986, IEEE Trans. Acoust. Speech Signal Process..

[11]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[12]  E. Hannan.  The Estimation of the Order of an ARMA Process , 1980 .

[13]  J. Rissanen.  A UNIVERSAL PRIOR FOR INTEGERS AND ESTIMATION BY MINIMUM DESCRIPTION LENGTH , 1983 .

[14]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[15]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[16]  D. Mitchell Wilkes,et al.  ARMA model order estimation based on the eigenvalues of the covariance matrix , 1993, IEEE Trans. Signal Process..

[17]  H. Akaike.  Fitting autoregressive models for prediction , 1969 .