R. K. Adenstedt, On Large-Sample Estimation for the Mean of a Stationary Random Sequence, The Annals of Statistics, vol.2, issue.6, pp.1095-1107, 1974.
DOI : 10.1214/aos/1176342867

H. Akaike, Statistical predictor identification, Annals of the Institute of Statistical Mathematics, vol.3, issue.1, pp.203-217, 1970.
DOI : 10.1007/BF02506337

R. Baillie, Long memory processes and fractional integration in econometrics, Journal of Econometrics, vol.73, issue.1, pp.5-59, 1996.
DOI : 10.1016/0304-4076(95)01732-1

J. Bardet, G. Lang, G. Oppenheim, A. Philippe, and M. Et-taqqu, Generators of long-range dependent processes : a survey, Theory and applications of long-range dependence, pp.579-623, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00127929

J. Barkoulas and C. Et-baum, Long-memory forecasting of US monetary indices, Journal of Forecasting, vol.16, issue.4, pp.291-302, 2006.
DOI : 10.1002/for.990

G. Baxter, An Asymptotic Result for the Finite Predictor., MATHEMATICA SCANDINAVICA, vol.10, pp.137-144, 1962.
DOI : 10.7146/math.scand.a-10520

J. Beran, Statistics for long-memory processes, volume 61 of Monographs on Statistics and Applied Probability, 1994.

J. Beran, R. Bhansali, and D. Et-ocker, On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes, Biometrika, vol.85, issue.4, pp.921-934, 1998.
DOI : 10.1093/biomet/85.4.921

K. Berk, Consistent Autoregressive Spectral Estimates, The Annals of Statistics, vol.2, issue.3, pp.489-502, 1974.
DOI : 10.1214/aos/1176342709

R. Bhansali, Asymptotic properties of the Wiener-Kolmogorov predictor. I, J. Roy. Statist. Soc. Ser. B, vol.36, pp.61-73, 1974.

R. Bhansali, Asymptotic properties of the Wiener-Kolmogorov predictor. II, J. Roy. Statist. Soc. Ser. B, vol.39, issue.1, pp.66-72, 1977.

R. Bhansali, Linear Prediction by Autoregressive Model Fitting in the Time Domain, The Annals of Statistics, vol.6, issue.1, pp.224-231, 1978.
DOI : 10.1214/aos/1176344081

R. Bhansali, L. Giraitis, and P. Et-kokoszka, Approximations and limit theory for quadratic forms of linear processes. Stochastic Process, Appl, vol.117, issue.1, pp.71-95, 2007.

R. Bhansali and P. Et-kokoszka, Prediction of long-memory time series : An overview, Estad?AsticaEstad? Estad?Astica, vol.53, pp.160-161, 2001.

R. J. Bhansali, L. Giraitis, and P. S. Et-kokoszka, Estimation of the memory parameter by fitting fractionally differenced autoregressive models, Journal of Multivariate Analysis, vol.97, issue.10, pp.972101-2130, 2006.
DOI : 10.1016/j.jmva.2006.01.003

P. Billingsley, Convergence of probability measures Wiley Series in Probability and Statistics : Probability and Statistics, 1999.

N. Bingham, C. Goldie, and J. Et-teugels, Regular variation. Encyclopedia of Mathematics and its applications, 1987.

A. Boettcher and J. Et-virtanen, Norms of Toeplitz Matrices with Fisher???Hartwig Symbols, SIAM Journal on Matrix Analysis and Applications, vol.29, issue.2, 2006.
DOI : 10.1137/06066165X

P. Bondon, Recursive Relations for Multistep Prediction of a Stationary Time Series, Journal of Time Series Analysis, vol.22, issue.4, pp.399-410, 2001.
DOI : 10.1111/1467-9892.00232

P. Bondon, Influence of Missing Values on the Prediction of a Stationary Time Series, Journal of Time Series Analysis, vol.10, issue.2, pp.519-525, 2005.
DOI : 10.1111/1467-9892.00191

P. Brockwell and R. Davis, Simple consistent estimation of the coefficients of a linear filter, Stochastic Processes and their Applications, 1988.
DOI : 10.1016/0304-4149(88)90063-4

P. Brockwell and R. Davis, Time Series : Theory and Methods, 1991.

P. Ciarlet, IntroductionàIntroduction`Introductionà l'analyse numérique matricielle etàet`età l'optimisation. Collection Mathématiques Appliquées pour la Maitrise, 1982.

R. Cleveland, W. Clevland, and J. Et-mcrae, Stl : A seasonal-trend decomposition procedure based on loess, Journal of Official Statistics, vol.6, pp.3-73, 1990.

N. Crato and B. Et-ray, Model selection and forecasting for long-range dependent processes, Journal of Forecasting, vol.14, issue.2, pp.107-125, 1996.
DOI : 10.1002/(SICI)1099-131X(199603)15:2<107::AID-FOR612>3.0.CO;2-D

R. Dahlhaus, Efficient parameter estimation for self-similar processes. The Annals of Statistics, 1989.

R. Deo, M. Hsieh, and C. Et-hurvich, Long memory in intertrade durations, counts and realized volatility of NYSE stocks, Journal of Statistical Planning and Inference, vol.140, issue.12, 2007.
DOI : 10.1016/j.jspi.2010.04.037

J. Doornik and M. Et-ooms, Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation, Studies in Nonlinear Dynamics & Econometrics, vol.8, issue.2, 2004.
DOI : 10.2202/1558-3708.1218

G. Fay and A. Et-philippe, Goodness-of-fit test for long range dependent processes, ESAIM: Probability and Statistics, vol.6, pp.239-258, 2001.
DOI : 10.1051/ps:2002013

R. Fox and M. S. Et-taqqu, Noncentral Limit Theorems for Quadratic Forms in Random Variables Having Long-Range Dependence, The Annals of Probability, vol.13, issue.2, pp.428-446, 1985.
DOI : 10.1214/aop/1176993001

R. Fox and M. S. Et-taqqu, Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series, The Annals of Statistics, vol.14, issue.2, pp.517-532, 1986.
DOI : 10.1214/aos/1176349936

R. Fox and M. S. Et-taqqu, Central limit theorems for quadratic forms in random variables having long-range dependence, Probability Theory and Related Fields, vol.4, issue.2, pp.213-240, 1987.
DOI : 10.1007/BF00569990

W. Fuller, Introduction to statistical time series, Wiley Series in Probability and Mathematical Statistics, 1976.
DOI : 10.1002/9780470316917

J. Geweke and S. Porter-hudak, THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS, Journal of Time Series Analysis, vol.50, issue.3, pp.221-238, 1983.
DOI : 10.1137/1010093

L. Giraitis, P. Kokoszka, and R. Et-leipus, STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM, Econometric Theory, vol.16, issue.01, pp.3-22, 2000.
DOI : 10.1017/S0266466600161018

L. Giraitis and D. Et-surgailis, 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, vol.10, issue.1, pp.87-104, 1990.
DOI : 10.1007/BF01207515

F. Godet, Linear prediction of long-range dependent time series, ESAIM: Probability and Statistics, vol.13, p.702485, 2007.
DOI : 10.1051/ps:2008015
URL : https://hal.archives-ouvertes.fr/hal-00131530

F. Godet, Prediction of long memory processes on same-realisation, Journal of Statistical Planning and Inference, vol.140, issue.4, 1922.
DOI : 10.1016/j.jspi.2009.09.016
URL : https://hal.archives-ouvertes.fr/hal-00196208

F. Godet, Linear prediction of long-range dependent time series, ESAIM: Probability and Statistics, vol.13, 2008.
DOI : 10.1051/ps:2008015
URL : https://hal.archives-ouvertes.fr/hal-00131530

H. Gray, N. Zhang, and W. Et-woodward, ON GENERALIZED FRACTIONAL PROCESSES, Journal of Time Series Analysis, vol.7, issue.12, pp.233-257, 1989.
DOI : 10.2307/2287515

U. Grenander and G. Et-szegö, Toeplitz forms and their applications. California Monographs in Mathematical Sciences, 1958.

J. Hidalgo and P. Et-soulier, Estimation of the location and exponent of the spectral singularity of a long memory process, Journal of Time Series Analysis, vol.23, issue.1, pp.55-81, 2004.
DOI : 10.1017/S0266466600161031
URL : https://hal.archives-ouvertes.fr/hal-00147620

J. Hidalgo and Y. Et-yajima, PREDICTION AND SIGNAL EXTRACTION OF STRONGLY DEPENDENT PROCESSES IN THE FREQUENCY DOMAIN, Econometric Theory, vol.18, issue.03, pp.584-624, 2002.
DOI : 10.1017/S0266466602183022

J. Hosking, Fractional differencing, Biometrika, vol.68, issue.1, pp.165-176, 1981.
DOI : 10.1093/biomet/68.1.165

J. Hosking, Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series, Journal of Econometrics, vol.73, issue.1, pp.261-284, 1996.
DOI : 10.1016/0304-4076(95)01740-2

J. R. Hosking, Modeling persistence in hydrological time series using fractional differencing, Water Resources Research, vol.6, issue.12, pp.1898-1908, 1984.
DOI : 10.1029/WR020i012p01898

H. Hurst, Long-term storage capacity of reservoirs, Trans. Am. Soc. Civ. Eng, vol.116, pp.770-799, 1951.

C. Ing and C. Wei, On same-realization prediction in an infinite-order autoregressive process, Journal of Multivariate Analysis, vol.85, issue.1, pp.130-155, 2003.
DOI : 10.1016/S0047-259X(02)00029-5

A. Inoue, Regularly varying correlation functions and KMO-Langevin equations, Hokkaido Mathematical Journal, vol.26, issue.2, pp.457-482, 1997.
DOI : 10.14492/hokmj/1351257978

A. Inoue, Asymptotics for the partial autocorrelation function of a stationary process, Journal d'Analyse Math??matique, vol.22, issue.1, pp.65-109, 2000.
DOI : 10.1007/BF02788986

A. Inoue and Y. Et-kasahara, Explicit representation of finite predictor coefficients and its applications, The Annals of Statistics, vol.34, issue.2, pp.973-993, 2006.
DOI : 10.1214/009053606000000209

A. Kolmogorov, Stationary sequences in Hilbert's space, Bull. Mosk. Gos. Univ. Mat, vol.2, issue.6, pp.1-40, 1941.

N. Kunitomo and T. Et-yamamoto, Properties of Predictors in Misspecified Autoregressive Time Series Models, Journal of the American Statistical Association, vol.36, issue.392, pp.941-950, 1985.
DOI : 10.1080/01621459.1985.10478208

H. Künsch, Statistical aspects of self-similar processes, Proceedings of the 1st World Congress of the Bernoulli Society, pp.67-74, 1986.

R. Lewis and G. C. Et-reinsel, Prediction of multivariate time series by autoregressive model fitting, Journal of Multivariate Analysis, vol.16, issue.3, pp.393-411, 1985.
DOI : 10.1016/0047-259X(85)90027-2

P. Major, Multiple Wiener-Itô integrals, Lecture Notes in Mathematics, vol.849, 1981.

A. Montanari, R. Rosso, and M. Et-taqqu, Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation, Water Resources Research, vol.2, issue.5, pp.1035-1044, 1997.
DOI : 10.1029/97WR00043

E. Moulines and P. Et-soulier, Broadband log-periodogram regression of time series with long-range dependence, The Annals of Statistics, vol.27, issue.4, pp.1415-1439, 1999.
DOI : 10.1214/aos/1017938932

M. Pourahmadi, On the convergence of finite linear predictors of stationary processes, Journal of Multivariate Analysis, vol.30, issue.2, pp.167-180, 1989.
DOI : 10.1016/0047-259X(89)90033-X

M. Pourahmadi, Foundations of time series analysis and prediction theory, Wiley Series in Probability and Statistics : Applied Probability and Statistics, 2001.

B. Ray, Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model, International Journal of Forecasting, vol.9, issue.2, pp.255-269, 1993.
DOI : 10.1016/0169-2070(93)90009-C

B. Ray, MODELING LONG-MEMORY PROCESSES FOR OPTIMAL LONG-RANGE PREDICTION, Journal of Time Series Analysis, vol.27, issue.3, pp.511-525, 1993.
DOI : 10.1016/0304-4076(92)90084-5

M. Rosenblatt, Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.40, issue.2, pp.125-132, 1979.
DOI : 10.1007/BF00534252

B. Simon, Orthogonal polynomials on the unit circle, 2005.

M. Taqqu, Fractional Brownian motion and long-range dependence, Theory and applications of long-range dependence, pp.5-38, 2003.

G. Tiao and R. Et-tsay, Some advances in non-linear and adaptive modelling in time-series, Journal of Forecasting, vol.84, issue.2, pp.109-131, 1994.
DOI : 10.1002/for.3980130206

K. Triantafyllopoulos, On the central moments of the multidimensional Gaussian distribution, Math. Sci, vol.28, issue.2, pp.125-128, 2003.

M. Viano, C. Deniau, and G. Et-oppenheim, LONG-RANGE DEPENDENCE AND MIXING FOR DISCRETE TIME FRACTIONAL PROCESSES, Journal of Time Series Analysis, vol.6, issue.2, pp.323-338, 1995.
DOI : 10.1111/j.1467-9892.1995.tb00237.x

C. Wei, Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series, The Annals of Statistics, vol.15, issue.4, pp.1667-1682, 1987.
DOI : 10.1214/aos/1176350617

P. Whittle, Prediction and regulation by linear least-square methods, 1983.

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series. With Engineering Applications. The Technology Press of the Massachusetts Institute of Technology, 1949.

W. Willinger, M. Taqqu, R. Sherman, and D. Et-wilson, Self-similarity through high-variability : Statistical analysis of ethernet lan traffic at the spurce level, Transactions on Networking, 1997.