Wavelet-Based Estimation of Anisotropic Spatiotemporal Long-Range Dependence

References

• Abry , P. , and Veitch , D. 1998 . Wavelet analysis of long-range dependence . IEEE Trans. Inform. Theory 44 : 2 – 15 .
   Web of Science ®Google Scholar
• Abry , P. , Veitch , D. , and Flandrin , P. 1998 . Long-range dependence: Revisiting aggregation with wavelets . J. Time Ser. Anal. 19 : 218 – 243 .
   Google Scholar
• Akkaya , A.D. , and Yücemen , M.S. 2002 . Stochastic modeling of earthquake occurrences and estimation of seismic hazard: a random field approach . Prob. Eng. Mech. 17 : 1 – 13 .
   Google Scholar
• Amann , H. 2009 . Anisotropic Function Spaces and Maximal Regularity for Parabolic Problems. Part 1: Function Spaces; Jindrich Necas Center for Mathematical Modeling Lecture Notes, Vol. 6, Prague .
   Google Scholar
• Anh , V.V. , and Inoue , A. 2005 . Financial markets with memory I: Dynamic models . Stoch. Anal. Appl. 23 : 275 – 300 .
   Web of Science ®Google Scholar
• Anh , V.V. , Leonenko , N.N. , and Sakhno , L.M. 2004 . On a class of minimum contrast estimators for fractional stochastic processes and fields . J. Statist. Plann. Infer. 123 : 161 – 185 .
   Web of Science ®Google Scholar
• Anh , V.V. , Leonenko , N.N. , and Sakhno , L.M. 2007 . Minimum contrast estimation of random processes based on information of second and third orders . J. Statist. Plann. Infer. 137 : 1302 – 1331 .
   Web of Science ®Google Scholar
• Avram , F. , and Brown , L. 1989 . A generalized Hölder inequality and a generalized Szego theorem . Proc. Amer. Mat. Soc. 107 : 687 – 695 .
   Web of Science ®Google Scholar
• Avram , F. , Leonenko , N.N. , and Sakhno , L.M. 2010 . On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality and the asymptotic theory of integrals and quadratic forms of stationary fields . ESAIM: Probability and Statistics 14 : 210 – 255 .
   Web of Science ®Google Scholar
• Bardet , J.M. , Lang , G. , Oppenheim , G. , Philippe , A. , Stoev , S. , and Taqqu , M.S. 2003 . Semi-parametric estimation of the long-range dependence parameter . In Theory and Applications of Long-Range Dependence ; Doukhan , P. , Oppenheim , G. , and Taqqu , M. (eds.), Birkhäuser , Boston , pp. 557 – 577 .
   Google Scholar
• Beran , J. 1994 . Statistics for Long-Memory Processes . Monographs on Statistics and Applied Probability 61 ; Chapman and Hall , London .
   Google Scholar
• Chan , G. , and Wood , A.T.A. 2000 . Increment-based estimators of fractal dimension for two-dimensional surface data . Statist. Sinica 10 : 343 – 376 .
   Web of Science ®Google Scholar
• Fay , G. , Moulines , E. , Roueff , F. , and Taqqu , M.S. 2009. Estimators of long-memory: Fourier versus wavelets. J. Econom. 15:159–177.
   Google Scholar
• Dachkovski , S. 2003 . Anisotropic function spaces and related semilinear hypoelliptic equations . Math. Nachr. 248–249 : 40 – 61 .
   Google Scholar
• Frías , M.P. , and Ruiz-Medina , M.D. 2011 . Computing functional estimators of the long-range dependence parameters in the spectral-wavelet domain . J. Statist. Plann. Infer. 141 ( 7 ): 2417 – 2427 .
   Google Scholar
• Frías , M.P. , Ruiz-Medina , M.D. , Alonso , F.J. , and Angulo , J.M. 2006 . Semiparametric estimation of spatiotemporal anisotropic long-range dependence. In Proceedings in Computational Statistics (COMPSTAT2006), Rome .
   Google Scholar
• Frías , M.P. , Ruiz-Medina , M.D. , Alonso , F.J. , and Angulo , J.M. 2006 . Spatiotemporal generation of long- range dependence models and estimation . Environmetrics 17 : 139 – 146 .
   Web of Science ®Google Scholar
• Frías , M.P. , Ruiz-Medina , M.D. , Alonso , F.J. , and Angulo , J.M. 2008 . Parameter estimation of self-similar spatial covariogram models . Commun. Statist.- Theory and Methods 37 : 1011 – 1023 .
   Web of Science ®Google Scholar
• Frías , M.P. , Ruiz-Medina , M.D. , Alonso , F.J. , and Angulo , J.M. 2009 . Spectral-marginal-based estimation of spatiotemporal long-range dependence . Commun. Statist.- Theory and Methods 38 : 103 – 114 .
   Google Scholar
• Gao , J. , Anh , V.V. , and Heyde , C.C. 2002 . Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency . Statist. Probab. Lett. 99 : 295 – 321 .
   Google Scholar
• Geweke , J. , and Porter-Hudak , S. 1983 . The estimation and application of long memory time series models . J. Time Ser. Anal. 4 : 221 – 238 .
   Google Scholar
• Grecksch , W. , Roth , C. , and Anh , V.V. 2009 . Q-fractional Brownian motion in infinite dimensions with application to fractional Black-Scholes market . Stoch. Anal. Appl. 27 : 149 – 175 .
   Web of Science ®Google Scholar
• Heyde , C.C. , and Yang , Y. 1997 . On defining long-range dependence . J. Appl. Prob. 34 : 939 – 944 .
   Web of Science ®Google Scholar
• Ivanov , A.V. , and Leonenko , N.N. 2004 . Asymptotic theory for non-linear regression with long-range dependence . Math. Method Statist. 13 : 153 – 178 .
   Google Scholar
• Ivanov , A.V. , and Leonenko , N.N. 2008 . Semiparametric analysis of long-range dependence in nonlinear regression . J. Statist. Plann. Infer. 138 : 1733 – 1753 .
   Web of Science ®Google Scholar
• Kelbert , M. , Leonenko , N.N. , and Ruiz-Medina , M.D. 2005 . Fractional random fields associated with stochastic fractional heat equation . Adv. Appl. Probab. 37 : 108 – 133 .
   Web of Science ®Google Scholar
• Leonenko , N.N. , and Sakhno , L.M. 2006 . On the Whittle estimators for some classes of continuous-parameter random processes and fields . Statist. Probab. Lett. 76 : 781 – 795 .
   Web of Science ®Google Scholar
• Lo , A.W. 1991 . Long-term memory in stock market prices . Econometrica 59 : 1279 – 1313 .
   Web of Science ®Google Scholar
• Lobato , I.N. , and Velasco , C. 2000 . Long memory in stock-market trading volume . J. Bus. Econ. Stat. 18 : 410 – 427 .
   Web of Science ®Google Scholar
• Ludeña , C. 2000 . Parametric estimation for Gaussian long-range dependent processes based on the log-periodogram . Bernoulli 6 : 709 – 728 .
   Web of Science ®Google Scholar
• Ma , C. 2003 . Power-law correlations and other models with long-range dependence on a lattice . J. Appl. Prob. 40 : 690 – 703 .
   Google Scholar
• Marguerit , C. , Schertzer , D. , Schmitt , F. , and Lovejoy , S. 1998. Copepod diffusion within multifractal phytoplankton fields. J. Marine Syst. 16:69–83.
   Web of Science ®Google Scholar
• Pesquet-Popescu , B. , and Lévy-Véhel , J. 2002 . Stochastics fractal models for image processing . IEEE Sig. Proc. Mag. 19 : 48 – 62 .
   Web of Science ®Google Scholar
• Robinson , P.M. 1994 . Semiparametric analysis of long memory time series . Ann. Statist. 22 : 515 – 539 .
   Web of Science ®Google Scholar
• Robinson , P.M. 1995 . Log-periodogram regression of time series with long range dependence . Ann. Statist. 23 : 1048 – 1072 .
   Web of Science ®Google Scholar
• Robinson , P.M. 1995 . Gaussian semiparametric estimation of long range dependence . Ann. Statist. 23 : 1630 – 1661 .
   Web of Science ®Google Scholar
• Roueff , F. , and Taqqu , M.S. 2009 . Asymptotic normality of wavelet estimation of the memory parameter for linear processes . J. Time Ser. Anal. 30 : 534 – 558 .
   Web of Science ®Google Scholar
• Stein , E.M. 1970 . Singular Integrals and Differential Properties of Functions . Princeton University Press , Princeton , NJ .
   Google Scholar
• Triebel , H. 1997 . Fractals and Spectra . Birkhäuser , Basel .
   Google Scholar
• Wornell , G.W. , and Oppenheim , A.V. 1992 . Estimation of fractal signals from noisy measurements using wavelets . IEEE Trans. Sig. Proc. 40 : 611 – 623 .
   Web of Science ®Google Scholar