P. Abry and D. Veitch, Wavelet analysis of long-range-dependent traffic, IEEE Transactions on Information Theory, vol.44, issue.1, pp.2-15, 1998.
DOI : 10.1109/18.650984

T. G. Andersen, T. Bollerslev, F. X. Diebold, and P. Labys, Modeling and Forecasting Realized Volatility, Econometrica, vol.71, issue.2, pp.579-625, 2003.
DOI : 10.1111/1468-0262.00418

J. Beran, On parameter estimation for locally stationary long-memory processes, Journal of Statistical Planning and Inference, vol.139, issue.3, pp.900-915, 2009.
DOI : 10.1016/j.jspi.2008.05.047

R. Dahlhaus, On the Kullback-Leibler information divergence of locally stationary processes. Stochastic Process, Appl, vol.62, issue.1, pp.139-168, 1996.

R. Dahlhaus, Fitting time series models to non-stationary processes, Annals of Statistics, vol.25, pp.1-37, 1997.

R. Dahlhaus, processes, The Annals of Statistics, vol.28, issue.6, pp.1762-1794, 2000.
DOI : 10.1214/aos/1015957480

URL : https://hal.archives-ouvertes.fr/hal-01095661

R. Dahlhaus, Local inference for locally stationary time series based on the empirical spectral measure, Journal of Econometrics, vol.151, issue.2, pp.101-112, 2009.
DOI : 10.1016/j.jeconom.2009.03.002

URL : https://hal.archives-ouvertes.fr/hal-00577962

R. Dahlhaus and M. Neumann, Locally adaptive fitting of semiparametric models to nonstationary time series. Stochastic Process, Appl, vol.91, issue.2, pp.277-308, 2001.

R. Dahlhaus and S. Subba-rao, Statistical inference for time-varying ARCH processes, The Annals of Statistics, vol.34, issue.3, pp.1075-1114, 2006.
DOI : 10.1214/009053606000000227

Z. Ding, R. Engle, and C. Granger, A long memory property of stock market returns and a new model, Journal of Empirical Finance, vol.1, issue.1, pp.83-106, 1993.
DOI : 10.1016/0927-5398(93)90006-D

Z. Ding and C. W. Granger, Modeling volatility persistence of speculative returns: A new approach, Journal of Econometrics, vol.73, issue.1, pp.185-215, 1996.
DOI : 10.1016/0304-4076(95)01737-2

Z. Ding, C. W. Granger, and R. F. Engle, A long memory property of stock market returns and a new model, Journal of Empirical Finance, vol.1, issue.1, pp.83-106, 1993.
DOI : 10.1016/0927-5398(93)90006-D

G. Fa¨yfa¨y, E. Moulines, F. Roueff, and M. Taqqu, Estimators of long-memory: Fourier versus wavelets, J. of Econometrics, 2009.

G. Fa¨yfa¨y, F. Roueff, and P. Soulier, Estimation of the memory parameter of the infinite-source Poisson process, Bernoulli, vol.13, issue.2, pp.473-491, 2007.
DOI : 10.3150/07-BEJ5123

P. Fryzlewicz, T. Sapatinas, and S. Subba-rao, Normalized least-squares estimation in time-varying ARCH models, The Annals of Statistics, vol.36, issue.2, pp.742-786, 2008.
DOI : 10.1214/07-AOS510

D. Guégan and Z. Lu, Wavelet methods for locally stationary seasonal long memory processes, CES Working Paper, 2009.

N. Haldrup and M. Ø. Nielsen, A regime switching long memory model for electricity prices, Journal of Econometrics, vol.135, issue.1-2, pp.349-376, 2006.
DOI : 10.1016/j.jeconom.2005.07.021

M. J. Jensen and B. Whitcher, Time-varying long memory in volatility: Detection and estimation with wavelets, preprint, 2000.

T. Mikosch and C. St?-aric?-a, Changes of structure in financial time series and the Garch model, REVSTAT, vol.2, issue.1, pp.41-73, 2004.

E. Moulines, P. Priouret, and F. Roueff, On recursive estimation for time varying autoregressive processes, The Annals of Statistics, vol.33, issue.6, pp.2610-2654, 2005.
DOI : 10.1214/009053605000000624

URL : https://hal.archives-ouvertes.fr/hal-00022067

E. Moulines, F. Roueff, and M. Taqqu, CENTRAL LIMIT THEOREM FOR THE LOG-REGRESSION WAVELET ESTIMATION OF THE MEMORY PARAMETER IN THE GAUSSIAN SEMI-PARAMETRIC CONTEXT, Fractals, vol.15, issue.04, pp.301-313, 2007.
DOI : 10.1142/S0218348X07003721

URL : https://hal.archives-ouvertes.fr/hal-00536394

E. Moulines, F. Roueff, and M. Taqqu, A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series, The Annals of Statistics, vol.36, issue.4, pp.1925-1956, 2008.
DOI : 10.1214/07-AOS527

URL : https://hal.archives-ouvertes.fr/hal-00016446

E. Moulines, F. Roueff, and M. S. Taqqu, On the Spectral Density of the Wavelet Coefficients of Long-Memory Time Series with Application to the Log-Regression Estimation of the Memory Parameter, Journal of Time Series Analysis, vol.8, issue.2, 2007.
DOI : 10.2307/2669763

URL : https://hal.archives-ouvertes.fr/hal-00016357

B. K. Ray and R. S. Tsay, Bayesian methods for change-point detection in long-range dependent processes, Journal of Time Series Analysis, vol.19, issue.5, pp.687-705, 2002.
DOI : 10.1016/S0378-3758(01)00075-1

P. M. Robinson, Gaussian Semiparametric Estimation of Long Range Dependence, The Annals of Statistics, vol.23, issue.5, pp.1630-1661, 1995.
DOI : 10.1214/aos/1176324317

P. M. Robinson, Log-Periodogram Regression of Time Series with Long Range Dependence, The Annals of Statistics, vol.23, issue.3, pp.1048-1072, 1995.
DOI : 10.1214/aos/1176324636

M. Rosenblatt, Stationary sequences and random fields, 1985.
DOI : 10.1007/978-1-4612-5156-9

F. Roueff and M. S. Taqqu, Asymptotic normality of wavelet estimators of the memory parameter for linear processes, Journal of Time Series Analysis, vol.50, issue.9, pp.534-558, 2009.
DOI : 10.1111/j.1467-9892.2009.00627.x

URL : https://hal.archives-ouvertes.fr/hal-00277645

F. Roueff and M. S. Taqqu, Central limit theorems for arrays of decimated linear processes, Stochastic Processes and their Applications, vol.119, issue.9, pp.3006-3041, 2009.
DOI : 10.1016/j.spa.2009.03.009

URL : https://hal.archives-ouvertes.fr/hal-00277643

G. Samorodnitsky, Long Range Dependence, Foundations and Trends?? in Stochastic Systems, vol.1, issue.3, pp.163-257, 2006.
DOI : 10.1561/0900000004

S. Wang, C. Hsiao, and L. Bauwens, Forecasting long-memory processes subject to structural breaks, 2008.

G. W. Wornell and A. V. Oppenheim, Estimation of fractal signals from noisy measurements using wavelets, IEEE Transactions on Signal Processing, vol.40, issue.3, pp.611-623, 1992.
DOI : 10.1109/78.120804

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