Model order selection of an autoregrssive model
[FPE,AIC,BIC,SBC,MDL,CAT,PHI,optFPE,optAIC,optBIC,optSBC,optMDL,optCAT,optPHI]=selmo(E,N);
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
REFERENCES:
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)"