Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 26, 1995 - Issue 4
67
Views
23
CrossRef citations to date
0
Altmetric
Original Articles

Order Choice in Nonlinear Autoregressive Models

Pages 307-328 | Received 21 May 1993, Accepted 26 Oct 1993, Published online: 27 Jun 2007

References

  • Auestad , B. and Tjostheim , D. 1990 . Identification of nonlinear time series: First order characterization and order determination . Biometrika , 77 : 669 – 681 .
  • Akaike , H. 1969 . Fitting autoregressive models for prediction . Ann. Inst. Statist. Math. , 21 : 243 – 247 .
  • Akaike , H. 1970 . Statistical predictor identification . Ann. Inst. Statist. Math. , 22 : 203 – 217 .
  • Akaike , H. 1979 . A Bayesian extension of the minimum AIC procedure for autoregressive model fitting . Biometrika , 66 : 237 – 242 .
  • Bickel , P. and Zhang , P. 1992 . Variable selection in nonparametric regression with categorical covariates . J. Amer. Statist. Assoc. , 87 : 90 – 97 .
  • Burman , P. and Nolan , D. 1992 . Data dependent estimation of prediction functions . J. Time Ser. Anal. , 13 : 3
  • Cheng , B. and Tong , H. 1992 . On consistent nonparametric order determination and chaos . J. Roy. Statist. Soc. , B, 54 : 427 – 449 .
  • Collomb , G. 1981 . Estimation non paramétrique de la régression . Inter. Statist. Review , 49 : 75 – 93 .
  • Collomb , G. 1984 . Propriétés de convergence presque complète du prédicteur à noyau . Z. Wahrsch. Verw. Gebiete , 66 : 441 – 460 .
  • Daukhan , P. 1994 . “ Mixing: properties and examples ” . In Lecture Notes in Statistics , Vol. 85 , Springer-Verlag .
  • Delecroix , M. 1987 . “ Sur l'estimation non paramétrique des processus ergodiques ” . France Thesis at Univ. Lille-Flandres-Artois
  • Ferre , L. 1990 . “ A mean square error criterion for determining a useful number of componants in some generalized PCA ” . In Public. Lab. Statist. et Probabilités , U.P.S. Taulouse .
  • Gasser , T. , Kneip , A. and Kohler , W. 1991 . A flexible and fast method for automatic smoothing . J. Amer. Statist. Assoc. , 86 : 643 – 653 .
  • Györfi , L. , Härdle , W. , Sarda , P. and Vieu , P. 1989 . Nonparametric curve estimation from Time Series , Vol. 60 , Springer- Verlag . Lecture Notes in Statistics
  • Hannan , E. 1980 . The estimation of the order of an ARMA process . Ann. Statist. , 8 : 1071 – 1081 .
  • Hannan , E. 1981 . Estimating the dimension of a linear system . J. Multivariate Anal , 11 : 459 – 473 .
  • Hannan , E. and Kavalieris , L. 1986 . Regression, autoregression models . J. Time Series Anal. , 27 : 27 – 47 .
  • Hannan , E. and Quinn , E. 1979 . The determination of the order of an autoregression . J. Roy, Statist. Soc. , B, 1 : 190 – 195 .
  • Härdle , W. 1990 . Applied Nonparametric Regression , Boston : Oxford University Press .
  • Härdle , W. and Kelly , G. 1987 . Nonparametric kernel regression estimation. Optimal bandwidth choice . Statistics , 18 : 21 – 35 .
  • Härdle , W. and Mammen , E. 1990 . “ Bootstrap methods in nonparametric regression ” . In Nonparametric Functional Estimation , Edited by: Roussas , G. G. 111 – 125 . Kluwer Dordrecht .
  • Härdle , W. and Marron , J. S. 1985 . Optimal bandwidth selection rule in nonparametric regression . Ann. Statist. , 13 : 1465 – 1481 .
  • Härdle , W. and Vieu , P. 1992 . Kernel regression smoothing of time series . Journ. of Time Ser. Anal. , 13 : 209 – 232 .
  • Hart , J. and Vieu , P. 1990 . Data-driven bandwidth choice for density estimation based on dependent data . Ann. Statist. , 18 : 873 – 890 .
  • Jones , R. H. 1975 . Fitting autoregression . J. Amer. Statist. Assoc. , 70 : 590 – 592 .
  • Katz , R. W. 1981 . On some criteria for estimating the order of a Markov chain . Technometrics , 23 : 243 – 249 .
  • Ozaki , T. 1977 . On the order determination of ARIMA models . Appl. Statist. , 26 : 290 – 301 .
  • Parzen , E. 1974 . Some recent advances in time series modelling . IEEE Trans. Automatic Control , AC-19 : 723 – 730 .
  • Pötscher , B. M. 1983 . Order estimation in ARMA models by Lagrangian multiplier tests . Ann. Statist. , 11 : 872 – 885 .
  • Pötscher , B. M. 1990 . Estimation of autoregressive moving average order given an infinite number of models and approximation of spectral densities . J. Time Series Anal. , 11 : 166 – 179 .
  • Robinson , P. 1983 . Nonparametric estimators for time series . J. Time Series Anal. , 4 : 185 – 207 .
  • Rissanen , J. 1978 . Modeling by shortest data description . Automatrica , 14 : 465 – 471 .
  • Rosenblatt , M. . A central limit theorem and a strong mixing condition . Proc. Nat. Acad. Sci. USA . Vol. 42 , pp. 43 – 47 .
  • Roussas , G. “ Nonparametric regression estimation under mixing conditions ” . Preprint
  • Roussas , G. and Ioannides , D. 1988 . “ Probability bounds for sums in triangular arrays of random variables under mixing conditions ” . In Statistical Theory and Data Analysis II , Edited by: Matusita , K. 293 – 308 . Elsevier Sciences Publishers B. V. .
  • Schwarz , G. 1978 . Estimating the dimension of a model . Ann. Statist. , 6 : 461 – 464 .
  • Shibata , R. 1976 . Selection of the order of an autoregressive model by Akaike's information criterion . Biometrika , 63 117- 126
  • Shibata , R. 1980 . Asymptotically efficient selection of the order of the model for estimating parameters of a linear process . Ann. Statist. , 8 : 147 – 174 .
  • Silverman , B. W. 1985 . Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion) . J. Roy. Statist. Soc. , 47 : 1 – 52 .
  • Stone , C. 1982 . Optimal global rates of convergence in nonparametric regression . Ann. Statist. Assoc. , 10 : 1040 – 1043 .
  • Stone , M. 1979 . Comments on model selection criteria of Akaike and Schwarz . J. Roy. Statist. Soc , B, 2 : 276 – 278 .
  • Tong , H. 1975 . Determining the order of a Markov chain by Akaike's information criterion . J. Appl. Prob. , 12 : 488 – 497 .
  • Tran , L. T. 1990 . Kernel density estimation under dependence . Statist. Prob. Let. , 10 : 193 – 201 .
  • Truong , Y. and Stone , C. 1992 . Nonparametric function estimation involving time series . Ann. Statist. , 20 : 77 – 97 .
  • Vieu , P. 1991a . “ Smoothing techniques in Time Series Analysis ” . In Nonparametric Functional Estimation , Edited by: Roussas , G. G. 271 – 283 . Kluwer Dordrecht .
  • Vieu , P. 1991b . Quadratic errors for nonparametric estimates under dependence . J. Multiv. Anal. , 39 : 324 – 347 .
  • Vieu , P. 1993a . “ Bandwidth choices of kernel regression: a survey ” . In Computer Intensive Methods in Statistics , Edited by: Härdle , W. and Simar , L. Vol. 1 , Berlin : Physica Verlag . Statistics and Computing
  • Vieu , P. 1993b . Choice of regressors in nonparametric estimation . Comp. Statist. and Data Anal. , 17 : 575 – 594 .
  • Yakowitz , S. 1989 . Nonparametric density and regression estimation for Markov sequences without mixing assumptions . J. Multivariate Anal. , 30 : 124 – 136 .
  • Zhang , P. 1991 . Variable selection in nonparametric regression with continuous covariates . Ann. Statist. , 19 : 1869 – 1882 .
  • Zhang , P. 1992 . On the distributional properties of model selection criteria . J. Amer. Statist. Assoc. , 87 : 732 – 737 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.