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 & Lawrence 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.
  E. J. Hannan and B. G. Quinn, The Determination of the Order of an Autoregression, Journal of the Royal Statistical Society. 
        Series B (Methodological), Vol. 41, No. 2, (1979), pp. 190-195. 
        https://www.jstor.org/stable/2985032
  S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
  Marple, S. Lawrence, Jr. "Digital spectral analysis with applications", Englewood Cliffs, NJ, Prentice-Hall, Inc., 1987.
  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
  J. Rissanen, A Universal Prior for Integers and Estimation by Minimum Description Length, Ann. Statist. Volume 11, Number 2 (1983), 416-431.
	doi:10.1214/aos/1176346150
	https://www.jstor.org/stable/2240558
  J. Rissanen, Modeling By Shortest Data Description, Automatica, Vol. 14, pp. 465-471.
	https://doi.org/10.1016/0005-1098(78)90005-5
  Gideon Schwarz, Estimating the Dimension of a Model, Ann. Statist. Volume 6, Number 2 (1978), 461-464.
	https://www.jstor.org/stable/2958889
  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  "Über die Wahl der optimalen Modellordnung bei der Darstellung von stationären Zeitreihen mittels Autoregressivmodell als Basis der Analyse von EEG - Biosignalen mit Hilfe eines Digitalrechners", Habilitationschrift - Technische Universität 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)"

Package: tsa