Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2017 (2017), Article ID 1235979, 12 pages
https://doi.org/10.1155/2017/1235979
Research Article

Bootstrap Order Determination for ARMA Models: A Comparison between Different Model Selection Criteria

University of California San Diego (UCSD), San Diego, CA, USA

Correspondence should be addressed to Livio Fenga; ude.dscu@agnefl

Received 31 July 2016; Accepted 19 March 2017; Published 16 April 2017

Academic Editor: Ramón M. Rodríguez-Dagnino

Copyright © 2017 Livio Fenga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. E. Box and G. M. Jenkins, Times Series Analysis. Forecasting and Control, Holden-Day, San Francisco, Calif, USA, 1970. View at MathSciNet
  2. M. R. Forster, “Key concepts in model selection: performance and generalizability,” Journal of Mathematical Psychology, vol. 44, no. 1, pp. 205–231, 2000. View at Publisher · View at Google Scholar · View at Scopus
  3. E. E. Leamer, Specification Searches: Ad Hoc Inference with Experimental Data, John Wiley & Sons, New York, NY, USA, 1978. View at MathSciNet
  4. K. P. Burnham and D. Anderson, Model Selection and Multimodal Inference: A Practical Information-Theoretic Approach, Springer, New York, NY, USA, 2nd edition, 2002.
  5. H.-Y. Chung, K.-W. Lee, and J.-Y. Koo, “A note on bootstrap model selection criterion,” Statistics & Probability Letters, vol. 26, no. 1, pp. 35–41, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  6. L. Fenga and D. N. Politis, “Bootstrap-based ARMA order selection,” Journal of Statistical Computation and Simulation, vol. 81, no. 7, pp. 799–814, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. D. A. Freedman, “Bootstrapping regression models,” The Annals of Statistics, vol. 9, no. 6, pp. 1218–1228, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. S. Raho and R. Tibshirani, “Bootstrap model selection via the cost complexity parameter in regression,” Tech. Rep., University of Toronto, 1993. View at Google Scholar
  9. J. Shao, “Bootstrap model selection,” Journal of the American Statistical Association, vol. 91, no. 434, pp. 655–665, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, pp. 716–723, 1974. View at Google Scholar · View at MathSciNet
  11. H. Akaike, “Statistical predictor identification,” Annals of the Institute of Statistical Mathematics, vol. 22, pp. 203–217, 1970. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. H. Akaike, “Fitting autoregressive models for prediction,” Annals of the Institute of Statistical Mathematics, vol. 21, pp. 243–247, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. G. Schwarz, “Estimating the dimension of a model,” The Annals of Statistics, vol. 6, no. 2, pp. 461–464, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. E. Kass and A. E. Raftery, “Bayes factors,” Journal of the American Statistical Association, vol. 90, no. 430, pp. 773–795, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. E. J. Hannan, “The estimation of the order of an ARMA process,” The Annals of Statistics, vol. 8, no. 5, pp. 1071–1081, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  16. E. J. Hannan and B. G. Quinn, “The determination of the order of an autoregression,” Journal of the Royal Statistical Society, Series B, vol. 41, pp. 190–195, 1979. View at Google Scholar
  17. K. Torre, D. Delignie, and L. c. Lemoine, “Detection of long-range dependence and estimation of fractal exponents through ARFIMA modelling,” The British Journal of Mathematical and Statistical Psychology, vol. 60, no. 1, pp. 85–106, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. A. D. McQuarrie and C.-L. Tsai, “Outlier detections in autoregressive models,” Journal of Computational and Graphical Statistics, vol. 12, no. 2, pp. 450–471, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. A. J. Fox, “Outliers in time series,” Journal of the Royal Statistical Society. Series B. Methodological, vol. 34, pp. 350–363, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. P. Zhang, “Inference after variable selection in linear regression models,” Biometrika, vol. 79, no. 4, pp. 741–746, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. L. Breiman, “The little bootstrap and other methods for dimensionality selection in regression: X-fixed prediction error,” Journal of the American Statistical Association, vol. 87, no. 419, pp. 738–754, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. Chatfield, “Model uncertainty, data mining and statistical inference,” Journal of the Royal Statistical Society, Series A (Statistics in Society), vol. 158, no. 3, pp. 419–466, 1995. View at Google Scholar
  23. J. S. Hjorth, Computer Intensive Statistical Methods—Validation Model Selection and Bootstrap, Chapman & Hall, London, UK, 1994. View at MathSciNet
  24. T. Soderstrom and P. Stoica, System Identification, Prentice-Hall, Englewood Cliffs, NJ, USA, 1989.
  25. S. Kullback and R. A. Leibler, “On information and sufficiency,” Annals of Mathematical Statistics, vol. 22, no. 1, pp. 79–86, 1951. View at Publisher · View at Google Scholar · View at MathSciNet
  26. R. Shibata, “Asymptotically efficient selection of the order of the model for estimating parameters of a linear process,” The Annals of Statistics, vol. 8, no. 1, pp. 147–164, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  27. J. Shao, “An asymptotic theory for linear model selection,” Statistica Sinica, vol. 7, no. 2, pp. 221–264, 1997. View at Google Scholar · View at MathSciNet · View at Scopus
  28. Y. Yang, “Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation,” Biometrika, vol. 92, no. 4, pp. 937–950, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. H. Bozdogan, “Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions,” Psychometrika, vol. 52, no. 3, pp. 345–370, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. C. L. Mallows, “Some comments on Cp,” Technometrics, vol. 15, no. 4, pp. 661–675, 1973. View at Google Scholar
  31. P. Bühlmann, “Bootstraps for time series,” Statistical Science, vol. 17, no. 1, pp. 52–72, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  32. P. Bühlmann, “Sieve bootstrap for time series,” Bernoulli, vol. 3, no. 2, pp. 123–148, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  33. J. P. Kreiss, “Bootstrap procedures for AR (∞)—processes,” in Bootstrapping and Related Techniques, K. H. Jockel, G. Rothe, and W. Sendler, Eds., vol. 376 of Lecture Notes in Economics and Mathematical Systems, pp. 107–113, Springer, Berlin, Germany, 1992. View at Publisher · View at Google Scholar
  34. G. M. Ljung and G. E. P. Box, “On a measure of lack of fit in time series models,” Biometrika, vol. 65, no. 2, pp. 297–303, 1978. View at Publisher · View at Google Scholar · View at Scopus
  35. P. M. T. Broersen, “Automatic spectral analysis with time series models,” IEEE Transactions on Instrumentation and Measurement, vol. 51, no. 2, pp. 211–216, 2002. View at Publisher · View at Google Scholar · View at Scopus
  36. I. Chang, G. C. Tiao, and C. Chen, “Estimation of time series parameters in the presence of outliers,” Technometrics, vol. 30, no. 2, pp. 193–204, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  37. C. Chen and L. Liu, “Joint estimation of model parameters and outlier effects in time series,” Journal of the American Statistical Association, vol. 88, no. 421, pp. 284–297, 1993. View at Publisher · View at Google Scholar
  38. D. Peña, “Influential observations in time series,” Journal of Business and Economic Statistics, vol. 8, no. 2, pp. 235–241, 1990. View at Publisher · View at Google Scholar · View at Scopus
  39. A. G. Bruce and D. Martin, “Leave-k-out diagnostics for time series (with discussion),” Journal of the Royal Statistical Society, Series B, vol. 51, no. 3, pp. 363–424, 1989. View at Google Scholar
  40. V. c. Gomez and A. n. Maravall, “Estimation, prediction, and interpolation for nonstationary series with the Kalman filter,” Journal of the American Statistical Association, vol. 89, no. 426, pp. 611–624, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. L. M. Liu, G. Hudak, G. E. P. Box, M. E. Muller, and G. C. Tiao, The SCA Statistical System: Reference Manual for Forecasting and Time Series Analysis, Scientific Computing Associates, DeKalb, Ill, USA, 1986.
  42. M. A. Carnero, D. Peña, and E. Ruiz, “Outliers and conditional autoregressive heteroscedasticity in time series,” Estadística, vol. 53, pp. 143–213, 2001. View at Google Scholar