R. F. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol.50, issue.4, pp.987-1008, 1982.
DOI : 10.2307/1912773

R. F. Engle and V. K. Ng, Measuring and Testing the Impact of News on Volatility, The Journal of Finance, vol.19, issue.5, pp.1749-1778, 1993.
DOI : 10.1111/j.1540-6261.1993.tb05127.x

J. Fan and Q. Yao, Efficient estimation of conditional variance functions in stochastic regression, Biometrika, vol.85, issue.3, pp.645-660, 1998.
DOI : 10.1093/biomet/85.3.645

G. Fiorentini, G. Calzolari, and L. Panattoni, Analytic derivatives and the computation of GARCH estimates, Journal of Applied Econometrics, vol.51, issue.4, pp.399-417, 1996.
DOI : 10.1002/(SICI)1099-1255(199607)11:4<399::AID-JAE401>3.0.CO;2-R

J. Franke and M. Diagne, Estimating market risk with neural networks, Statistics & Decisions, vol.24, issue.2, pp.233-253, 2006.
DOI : 10.1524/stnd.2006.24.2.233

M. Garcin, Empirical wavelet coefficients and denoising of chaotic data in the phase space Handbook of applications of chaos theory, 2016.

M. Garcin, Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01399570

M. Garcin and D. Guégan, Probability density of the empirical wavelet coefficients of a noisy chaos, Physica D: Nonlinear Phenomena, vol.276, pp.28-47, 2014.
DOI : 10.1016/j.physd.2014.03.005

URL : https://hal.archives-ouvertes.fr/hal-01310473

M. Garcin and D. Guégan, Wavelet shrinkage of a noisy dynamical system with non-linear noise impact, Physica D: Nonlinear Phenomena, vol.325, pp.126-145, 2016.
DOI : 10.1016/j.physd.2016.03.013

URL : https://hal.archives-ouvertes.fr/halshs-01244239

M. Giaquinta, S. Hildebrandt, L. R. Glosten, R. Jagannathan, and D. Runkle, Calculus of variations. A series of comprehensive studies in mathematics, On the relationship between the expected value and the volatility of the nominal excess return on stocks, pp.1779-1801, 1993.

C. Gouriéroux and A. Monfort, Qualitative threshold ARCH models, Journal of Econometrics, vol.52, issue.1-2, pp.159-199, 1992.
DOI : 10.1016/0304-4076(92)90069-4

W. Härdle and A. Tsybakov, Local polynomial estimators of the volatility function in nonparametric autoregression, Journal of Econometrics, vol.81, issue.1, pp.223-242, 1997.
DOI : 10.1016/S0304-4076(97)00044-4

C. M. Hafner and O. Linton, Efficient estimation of a multivariate multiplicative volatility model, Journal of Econometrics, vol.159, issue.1, pp.55-73, 2010.
DOI : 10.1016/j.jeconom.2010.04.007

URL : https://hal.archives-ouvertes.fr/hal-00732539

H. Han and D. Kristensen, Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates, Journal of Business & Economic Statistics, vol.15, issue.3, pp.416-429, 2014.
DOI : 10.1007/BF00532676

H. Han, D. Kristensen, and F. Klaassen, Semiparametric multiplicative GARCH-X model: Adopting economic variables to explain volatility Improving GARCH volatility forecasts with regime-switching GARCH, Advances in Markov-Switching Models, pp.223-254, 2002.

O. Linton and E. Mammen, Estimating Semiparametric ARCH(oo) Models by Kernel Smoothing Methods1, Econometrica, vol.73, issue.3, pp.771-836, 2005.
DOI : 10.1111/j.1468-0262.2005.00596.x

S. Mallat, P. Malliavin, and A. B. Thalmaier, Une exploration des signaux en ondelettes, Ellipses, ´ Editions de l' ´ Ecole Polytechnique The variation of certain speculative prices, Stochastic calculus of variations in mathematical finance, pp.392-417, 1963.

D. B. Nelson, ARCH models as diffusion approximations, Journal of Econometrics, vol.45, issue.1-2, pp.7-38, 1990.
DOI : 10.1016/0304-4076(90)90092-8

D. B. Nelson, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, vol.59, issue.2, pp.347-370, 1991.
DOI : 10.2307/2938260

W. K. Newey and K. D. West, A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, vol.55, issue.3, pp.703-708, 1986.
DOI : 10.2307/1913610

A. R. Pagan and G. W. Schwert, Alternative models for conditional stock volatility, Journal of Econometrics, vol.45, issue.1-2, pp.267-290, 1990.
DOI : 10.1016/0304-4076(90)90101-X

A. J. Patton and K. Sheppard, Evaluating volatility and correlation forecasts Handbook of financial time series, pp.801-838, 2009.

L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, p.259268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

L. Rudin, P. L. Lions, and S. Osher, Multiplicative denoising and deblurring: Theory and algorithms Geometric level set methods in imaging, vision, and graphics, pp.103-119, 2003.

C. Stein, Estimation of the mean of a multivariate normal distribution, The Annals of statistics, pp.1135-1151, 1981.

L. Wang, C. Feng, Q. Song, and L. Yang, Efficient semiparametric garch modeling of financial volatility, Statistica Sinica, vol.22, issue.1, pp.249-270, 2012.
DOI : 10.5705/ss.2009.285

M. Weitzmann, Income, wealth, and the maximum principle, 2009.

K. D. West, Asymptotic Inference about Predictive Ability, Econometrica, vol.64, issue.5, pp.1067-1084, 1996.
DOI : 10.2307/2171956

K. Xu and P. Phillips, Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications, Journal of Business & Economic Statistics, vol.29, issue.4, pp.518-528, 2011.
DOI : 10.1198/jbes.2011.09012

Z. Zheng, Z. Qiao, T. Takaishi, H. E. Stanley, and B. Li, Realized Volatility and Absolute Return Volatility: A Comparison Indicating Market Risk, PLoS ONE, vol.51, issue.7, pp.10-1371, 2014.
DOI : 10.1371/journal.pone.0102940.g008

URL : http://doi.org/10.1371/journal.pone.0102940