Estimation of the memory parameter by fitting fractionally differenced autoregressive models

Journal of Multivariate Analysis

Volumn 97, Issue 10, 2006, Pages 2101-2130

  Bhansali, R J ^a   Giraitis, L ^b   Kokoszka, P S ^c  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b UNIVERSITY OF YORK   (United Kingdom)

^c UTAH STATE UNIVERSITY   (United States)

Author keywords

Autoregressive estimation; Long memory

Indexed keywords

EID: 33749121194     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2006.01.003     Document Type: Article

References (22)

1. Baxter G. An asymptotic result for the finite predictor. Math. Scand. 10 (1962) 137-144
2. Berk K.N. Consistent autoregressive spectral estimates. Ann. Statist. 2 (1974) 489-502
3. Bhansali R.J. Linear prediction by autoregressive model fitting in the time domain. Ann. Statist. 6 (1978) 224-231
4. Bhansali R.J. Autoregressive and window estimates of the inverse correlation function. Biometrika 67 (1980) 551-566
5. Bhansali R.J. Order selection for linear time series models: a review. In: Subba Rao T. (Ed). Developments in Time Series Analysis (1993), Chapman & Hall, London 50-56
6. R.J. Bhansali, L. Giraitis, P.S. Kokoszka, Approximations and limit theory for quadratic forms of linear processes, Technical Report, Utah State University, 2005.
7. Bhansali R.J., and Kokoszka P.S. Estimation of the long-memory parameter: a review and an extension. In: Basawa I.V., Heyde C.C., and Taylor R.L. (Eds). Proceedings of the Symposium on Inference for Stochastic Processes, IMS Lecture Notes (2001) 125-150
8. Bloomfield P. An exponential model for the spectrum of a scalar time series. Biometrika 60 (1973) 217-226
9. Brillinger D.R. Time Series: Data Analysis and Theory (1975), Holt, New York
10. Dahlhaus R. Efficient parameter estimation for self similar processes. Ann. Statist. 17 (1989) 1749-1766
11. Fox R., and Taqqu M.S. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 (1986) 517-532
12. Giraitis L., and Surgailis D. CLT for quadratic forms in strongly dependent linear variables and application to asymptotical normality of Whittle's estimate. Probab. Theory Related Fields 86 (1990) 87-104
13. Hurvich C.M., and Brodsky J. Broadband semiparametric estimation of the memory parameter of a long-memory time series using fractional exponential models. J. Time Ser. Anal. 23 (2001) 221-249
14. Kailath T., Vieira A., and Morf M. Inverses of Toeplitz operators, innovations, and orthogonal polynomials. SIAM Rev. 20 (1978) 106-119
15. Kokoszka P.S., and Taqqu M.S. Fractional ARIMA with stable innovations. Stochastic Process. Appl. 60 (1995) 19-47
16. Moulines E., and Soulier P. Broad band log-periodogram regression of time series with long range dependence. Ann. Statist. 27 (1999) 1415-1439
17. Moulines E., and Soulier P. Data-driven order selection for projection estimator of the spectral density of time series with long range dependence. J. Time Ser. Anal. 21 (2000) 193-218
18. Parzen E. Multiple time series modelling. In: Krishnaiah P.R. (Ed). Multivariate Analysis II (1969), Academic Press, New York
19. Rao C.R. Linear Statistical Inference (1973), Wiley, New York
20. Robinson P.M. Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 (1995) 1630-1661
21. Shibata R. Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Ann. Statist. 8 (1980) 147-164
22. Shibata R. An optimal autoregressive spectral estimate. Ann. Statist. 9 (1981) 300-306