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Model order selection of an autoregrssive model


function [FPE,AIC,BIC,SBC,MDL,CATcrit,PHI,optFPE,optAIC,optBIC,optSBC,optMDL,optCAT,optPHI,p,C]=selmo(e,NC);


 Model order selection of an autoregrssive model

 E    Error function E(p)
 N    length of the data set, that was used for calculating E(p)
 show  optional; if given the parameters are shown

 FPE    Final Prediction Error (Kay 1987, Wei 1990, Priestley 1981  -> Akaike 1969)
 AIC    Akaike Information Criterion (Marple 1987, Wei 1990, Priestley 1981 -> Akaike 1974)
 BIC    Bayesian Akaike Information Criterion (Wei 1990, Priestley 1981 -> Akaike 1978,1979)
 CAT    Parzen's CAT Criterion (Wei 1994 -> Parzen 1974)
 MDL    Minimal Description length Criterion (Marple 1987 -> Rissanen 1978,83)
 SBC    Schwartz's Bayesian Criterion (Wei 1994; Schwartz 1978)
 PHI    Phi criterion (Pukkila et al. 1988, Hannan 1980 -> Hannan & Quinn, 1979)
 HAR    Haring G. (1975)
 JEW    Jenkins and Watts (1968)

 optFPE     order where FPE is minimal
 optAIC     order where AIC is minimal
 optBIC     order where BIC is minimal
 optSBC     order where SBC is minimal
 optMDL     order where MDL is minimal
 optCAT     order where CAT is minimal
 optPHI     order where PHI is minimal

 usually is 
 AIC > FPE > *MDL* > PHI > SBC > CAT ~ BIC

  P.J. Brockwell and R.A. Davis 'Time Series: Theory and Methods', 2nd ed. Springer, 1991.
  S. Haykin 'Adaptive Filter Theory' 3ed. Prentice Hall, 1996.
  M.B. Priestley 'Spectral Analysis and Time Series' Academic Press, 1981. 
  C.E. Shannon and W. Weaver 'The mathematical theory of communication' University of Illinois Press, Urbana 1949 (reprint 1963).
  W.S. Wei 'Time Series Analysis' Addison Wesley, 1990.
  Jenkins G.M. Watts D.G 'Spectral Analysis and its applications', Holden-Day, 1968.
  G. Haring  '�er die Wahl der optimalen Modellordnung bei der Darstellung von station�en Zeitreihen mittels Autoregressivmodell als Basis der Analyse von EEG - Biosignalen mit Hilfe eines Digitalrechners', Habilitationschrift - Technische Universit� Graz, Austria, 1975.
                  (1)'About selecting the optimal model at the representation of stationary time series by means of an autoregressive model as basis of the analysis of EEG - biosignals by means of a digital computer)'


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