A derivation of the information criteria for selecting autoregressive models

On derive le critere d'information d'Akaike en adoptant −2T fois la densite predictive esperee d'une observation future

[1]  H. Akaike.  Statistical predictor identification , 1970 .

[2]  A. M. Walker.  Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series , 1964, Journal of the Australian Mathematical Society.

[3]  E. Hannan,et al.  Autocorrelation, Autoregression and Autoregressive Approximation , 1982 .

[4]  G. Baxter.  A norm inequality for a “finite-section” Wiener-Hopf equation , 1963 .

[5]  J. Kiefer,et al.  An Introduction to Stochastic Processes. , 1956 .

[6]  Optimal estimates of predictive distributions , 1980 .

[7]  U. Grenander,et al.  Statistical analysis of stationary time series , 1958 .

[8]  R. J. Bhansali,et al.  A Mixed Spectrum Analysis of the Lynx Data , 1979 .

[9]  N. Inagaki.  Two errors in statistical model fitting , 1977 .

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

[11]  Y. Ogata.  Maximum likelihood estimates of incorrect Markov models for time series and the derivation of AIC , 1980, Journal of Applied Probability.

[12]  R. Bhansali.  Effects of Not Knowing the Order of an Autoregressive Process on the Mean Squared Error of Prediction—I , 1981 .

[13]  U. Grenander,et al.  An extension of a theorem of G. Szegö and its application to the study of stochastic processes , 1954 .

[14]  G. Baxter.  An Asymptotic Result for the Finite Predictor. , 1962 .

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

[16]  Donald Poskitt,et al.  On the posterior odds of time series models , 1983 .

[17]  R. Shibata.  Asymptotically Efficient Selection of the Order of the Model for Estimating Parameters of a Linear Process , 1980 .

[18]  P. Whittle.  Prediction and Regulation by Linear Least-Square Methods , 1983 .

[19]  J. Aitchison.  Goodness of prediction fit , 1975 .

[20]  R. Bhansali.  Linear Prediction by Autoregressive Model Fitting in the Time Domain , 1978 .

[21]  S. Geisser,et al.  A Predictive Approach to Model Selection , 1979 .

[22]  E. J. Hannan,et al.  The Estimation of the Prediction Error Variance , 1977 .

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

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

[25]  R. Kashyap.  A Bayesian comparison of different classes of dynamic models using empirical data , 1977 .

[26]  G. Chow.  A comparison of the information and posterior probability criteria for model selection , 1981 .

[27]  H. T. Davis,et al.  Estimation of the Innovation Variance of a Stationary Time Series , 1968 .

[28]  R. Bhansali,et al.  Some properties of the order of an autoregressive model selected by a generalization of Akaike∘s EPF criterion , 1977 .

[29]  R. Bhansali.  THE CRITERION AUTOREGRESSIVE TRANSFER FUNCTION OF PARZEN , 1986 .

[30]  D. Spiegelhalter,et al.  Bayes Factors and Choice Criteria for Linear Models , 1980 .

[31]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[32]  A. Atkinson.  Likelihood ratios, posterior odds and information criteria , 1981 .

[33]  Ritei Shibata,et al.  CONVERGENCE OF LEAST SQUARES ESTIMATES OF AUTOREGRESSIVE PARAMETERS1 , 1977 .

[34]  Taku Yamamoto,et al.  Asymptotic mean square prediction error for an autoregressive model with estimated coefficients , 1976 .

[35]  R. Shibata.  An Optimal Autoregressive Spectral Estimate , 1981 .

[36]  A. Atkinson.  A note on the generalized information criterion for choice of a model , 1980 .

[37]  H. Akaike.  A Bayesian extension of the minimum AIC procedure of autoregressive model fitting , 1979 .

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

[39]  Takamitsu Sawa,et al.  Information criteria for discriminating among alternative regression models / BEBR No. 455 , 1978 .

[40]  H. Akaike.  Likelihood of a model and information criteria , 1981 .

[41]  R. Shibata.  Selection of the order of an autoregressive model by Akaike's information criterion , 1976 .

[42]  T. Ozaki.  On the Order Determination of Arima Models , 1977 .

[43]  M. Stone.  Comments on Model Selection Criteria of Akaike and Schwarz , 1979 .