References
- Chiriac R, Voev V. Modeling and forecasting multivariate realized volatility. J Appl Econ. 2011;26(6):922–947. doi: 10.1002/jae.1152
- Sowell F. Maximum likelihood estimation of fractionally integrated time series models. Working paper, Carnegie-Mellon University; 1989.
- Luceño A. A fast likelihood approximation for vector general linear processes with long series: application to fractional differencing. Biometrika. 1996;83(3):603–614. doi: 10.1093/biomet/83.3.603
- Tsay W-J. Maximum likelihood estimation of stationary multivariate ARFIMA processes. J Stat Comput Simul. 2010;80(7–8):729–745. doi: 10.1080/00949650902773536
- Fox R, Taqqu MS. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann Stat. 1986;14(2):517–532. doi: 10.1214/aos/1176349936
- Giraitis L, Surgailis D. A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotic normality of Whittle's estimate. Probab Theory Related Fields. 1990;86:87–104. doi: 10.1007/BF01207515
- Künsch H. Statistical aspects of self-similar processes. In Prokhorov Y, Sazanov VV, editors. Proceedings of the first world congress of the Bernoulli society; 1987. Utrecht: VNU Science Press. p. 67–74.
- Robinson PM. Gaussian semiparametric estimation of long range dependence. Ann Stat. 1995;23(5):1630–1661. doi: 10.1214/aos/1176324317
- Robinson PM. Log-periodogram regression of time series with long range dependence. Ann Stat. 1995;23(3):1048–1072. doi: 10.1214/aos/1176324636
- Lobato IN. A semiparametric two-step estimator in a multivariate long memory model. J Econ. 1999;90:129–153. doi: 10.1016/S0304-4076(98)00038-4
- Shimotsu K. Gaussian semiparametric estimation of multivariate fractionally integrated processes. J Econ. 2007;137:277–310. doi: 10.1016/j.jeconom.2006.01.003
- Nielsen FS. Local Whittle estimation of multi-variate fractionally integrated processes. J Time Series Anal. 2011;32(3):317–335. doi: 10.1111/j.1467-9892.2010.00702.x
- Grenander U. On empirical spectral analysis of stochastic process. Ark Mat. 1951;1:197–277.
- Priestley MB. Spectral analysis and time series. London: Academic Press; 1981.
- Hurvich CM, Beltrão KI. Asymptotics for the low-frequency ordinates of the periodogram of a long-memory time series. J Time Series Anal. 1993;14(5):455–472. doi: 10.1111/j.1467-9892.1993.tb00157.x
- Fryzlewicz P, Nason GP, von Sachs R. A Wavelet-Fisz approach to spectrum estimation. J Time Series Anal. 2008;29(5):868–880. doi: 10.1111/j.1467-9892.2008.00586.x
- Dahlhaus R. Spectral analysis with tapered data. J Time Series Anal. 1983;4:163–175. doi: 10.1111/j.1467-9892.1983.tb00366.x
- Hurvich CM, Ray BK. Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. J Time Series Anal. 1995;16(1):17–42. doi: 10.1111/j.1467-9892.1995.tb00221.x
- Velasco C. Gaussian semiparametric estimation of non-stationary time series. J Time Series Anal. 1999;20:87–127. doi: 10.1111/1467-9892.00127
- Olbermann BP, Lopes SRC, Reisen VA. Invariance of the first difference in ARFIMA models. Comput Stat. 2006;21(3):445–461. doi: 10.1007/s00180-006-0005-0
- Shimotsu K, Phillips PCB. Exact local Whittle estimation of fractional integration. Ann Stat. 2005;33(4):1890–1933. doi: 10.1214/009053605000000309
- Zygmund A. Trigonometric series. Vol. I, II. Cambridge: Cambridge University Press; 2002.