Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series

Annals of Statistics

Volumn 35, Issue 3, 2007, Pages 1238-1277

  Ing, Ching Kang ^a,b  

^a ACADEMIA SINICA   (Taiwan)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Accumulated prediction errors; Asymptotic efficiency; Asymptotic equivalence; Information criterion; Optimal forecasting; Order selection

Indexed keywords

EID: 49749104267     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000001550     Document Type: Article

References (31)

1. AKAIKE, H. (1974). A new look at the statistical model identification. IEEE Trans. Automatic Control 19 716-723. MR0423716
2. BHANSALI, R. J. (1986). Asymptotically efficient selection of the order by the criterion autoregressive transfer function. Ann. Statist. 14 315-325. MR0829571
3. FINDLEY, D. F. (2005). Asymptotic second moment properties of out-of-sample forecast errors of misspecifiedregARIMA models and the optimality of GLS. Statist. Sinica 15 447-476. MR2190214
4. FINDLEY, D. F. and WEI, C. Z. (1993). Moment bounds for deriving time series CLTs and model selection procedures. Statist. Sinica 3 453-480. MR 1243396
5. GOLDENSHLUGER, A. and ZEEVI, A. (2001). Nonasymptotic bounds for autoregressive time series modeling. Ann. Statist. 29 417-444. MR 1863964
6. HANNAN, E. J., MCDOUGALL, A. J. and POSKITT, D. S. (1989). Recursive estimation of autoregressions. J. Roy. Statist. Soc. Ser. B 51 217-233. MR1007454
7. HANNAN, E. J. and QUINN, B.C. (1979). The determination of the order of an autoregression. J. Roy. Statist. Soc. Ser. B 41 190-195. MR0547244
8. HEMERLY, E. M. and DAVIS, M. H. A. (1989). Strong consistency of the PLS criterion for order determination of autoregressive processes. Ann. Statist. 17 941-946. MR0994279
9. HURVICH, C. M. and TSAI, C.-L. (1989). Regression and time series model selection in small samples. Biometrika 76 297-307. MR1016020
10. ING, C. K. (2001). A note on mean-squared prediction errors of the least squares predictors in random walk models. J. Time Ser. Anal. 22 711-724. MR1867394
11. ING, C. K. (2003). Multistep prediction in autoregressive processes. Econometric Theory 19 254-279. MR1966030
12. ING, C. K. (2005). Accumulated prediction errors, information criteria, and optimal forecasting for autoregressive time series. Technical report, Inst. Statistical Science, Academia Sinica.
13. ING, C. K. and WEI, C. Z. (2003). On same-realization prediction in an infinite-order autoregressive process. J. Multivariate Anal. 85 130-155. MR1978181
14. ING, C. K. and WEI, C. Z. (2005). Order selection for same-realization predictions in autoregressive processes. Ann. Statist. 33 2423-2474. MR2211091
15. INOUE, A. and KILIAN, L. (2006). On the selection of forecasting models. J. Econometrics 130 273-306. MR2211796
16. KARAGRIGORIOU, A. (1997). Asymptotic efficiency of the order selection of a non-Gaussian AR process. Statist. Sinica 7 407-423. MR1466689
17. KAVALIERIS, L. (1989). The estimation of the order of an autoregression using recursive residuals and cross-validation. J. Time Ser. Anal. 10 271-281. MR 1028942
18. KUNITOMO, N. and YAMAMOTO, T. (1985). Properties of predictors in misspecified autoregressive time series models. J. Amer. Statist. Assoc. 80 941-950. MR0819598
19. LAI, T. L. and WEI, C.Z. (1982). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10 154-166. MR0642726
20. MCCRACKEN, M. W. (2000). Robust out-of-sample inference. J. Econometrics 99 195-223. MR1792249
21. RISSANEN, J. (1986). Order estimation by accumulated prediction errors. J. Appl. Probab. 23A 55-61. MR0803162
22. SCHORFHEIDE, F. (2005). VAR forecasting under misspecification. J. Econometrics 128 99-136. MR2022928
23. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464. MR0468014
24. SHIBATA, R. (1976). Selection of the order of an autoregressive model by Akaike's information criterion. Biometrika 63 117-126. MR0403130
25. SHIBATA, R. (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Ann. Statist. 8 147-164. MR0557560
26. SPEED, T. P. and YU, B. (1993). Model selection and prediction: Normal regression. Ann. Inst. Statist. Math. 45 35-54. MR1220289
27. WAX, M. (1988). Order selection for AR models by predictive least squares. IEEE Trans. Acoustics Speech and Signal Processing 36 581-588.
28. WEI, C. Z. (1987). Adaptive prediction by least squares predictors in stochastic regression models with applications to time series. Ann. Statist. 15 1667-1682. MR0913581
29. WEI, C. Z. (1992). On predictive least squares principles. Ann. Statist. 20 1-42. MR1150333
30. WEST, K. D. (1996). Asymptotic inference about predictive ability. Econometrica 64 1067-1084. MR1403232
31. ZHENG, X. and LOH, W.-Y. (1997). A consistent variable selection criterion for linear models with high-dimensional covariates. Statist. Sinica 7 311-325. MR1466685