Parametric Estimation

  • Jan Beran
Chapter

Abstract

Linear process

References

  1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov (Hrsg.) & F. Csáki (Eds.), Proceedings of the Second International Symposium on Information Theory (pp. 267–281). Budapest: Akademiai Kiado.Google Scholar
  2. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.MathSciNetCrossRefMATHGoogle Scholar
  3. Beran, J. (1986). Estimation, testing and prediction for self-similar and related processes. Ph.D. Thesis, ETH Zürich.Google Scholar
  4. Beran, J. (1995). Maximum likelihood estimation of the differencing parameter for invertible short and long-memory ARIMA models. Journal of the Royal Statistical Society, Series B, 57, 659–672.MathSciNetMATHGoogle Scholar
  5. Beran, J., Bhansali, R. J., & Ocker, D. (1998). On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes. Biometrika, 85(4), 921–934.Google Scholar
  6. Beran, J., Feng, Y., Ghosh, S., & Kulik, R. (2013). Long-memory processes. New York: Springer.Google Scholar
  7. Claeskens, G., & Hjort, N. L. (2008). Model selection and model averaging. Cambridge: Cambridge University Press.Google Scholar
  8. Dahlhaus, R. (1989). Efficient parameter estimation for self-similar processes. The Annals of Statistics, 17(4), 1749–1766.Google Scholar
  9. Fox, R., & Taqqu, M. S. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The Annals of Statistics, 14, 517–532.Google Scholar
  10. Giraitis, L., & Surgailis, D. (1990). A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle’s estimate. Probability Theory and Related Fields, 86(1), 87–104.Google Scholar
  11. Grenander, U., & Szegö, G. (1958). Toeplitz forms and their application. Berkeley: University of California Press.Google Scholar
  12. Hannan, E. J. (1973). Central limit theorems for time series regression. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 26, 157–170.Google Scholar
  13. Hannan, E. J., & Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B, 41(2), 190–195.Google Scholar
  14. Horváth, L., & Shao, Q.-M. (1999). Limit theorems for quadratic forms with applications to Whittle’s estimate. The Annals of Applied Probability, 9(1), 146–187.Google Scholar
  15. Hosoya, Y. (1997). A limit theory for long-range dependence and statistical inference on related models. The Annals of Statistics, 25(1), 105–137.MathSciNetCrossRefMATHGoogle Scholar
  16. McQuarrie, A. D., & Tsai, C. L. (1998). Regression and time series model selection. Singapore: World Scientific.Google Scholar
  17. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 2(6), 461–464.Google Scholar
  18. Shibata, R. (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. The Annals of Statistics, 8, 147–164.Google Scholar
  19. Shibata, R. (1981). An optimal autoregressive spectral estimate. The Annals of Statistics, 9, 300–306.Google Scholar
  20. Velasco, C., & Robinson, P. M. (2000). Whittle pseudo-maximum likelihood estimation for nonstationary time series. Journal of the American Statistical Association, 95(452), 1229–1243.Google Scholar
  21. Yajima, Y. (1985). On estimation of long-memory time series models. Australian Journal of Statistics, 27(3), 303–320.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Jan Beran
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany

Personalised recommendations