Maximum-likelihood estimators and random walks in long memory models

References

• Beran , J. 1994 . Statistics for Long-Memory Processes , New York : Chapman and Hall .
   Google Scholar
• Embrechts , P. and Maejima , M. 2002 . Selfsimilar Processes , Princeton , NY : Princeton University Press .
   Google Scholar
• Samorodnitsky , G. and Taqqu , M. 1994 . Stable Non-Gaussian Random Variables , London : Chapman and Hall .
   Google Scholar
• Nualart , D. 2006 . Malliavin Calculus and Related Topics , 2 , New York : Springer .
   Google Scholar
• Dobrushin , R. L. and Major , P. 1979 . Non-central limit theorems for non-linear functionals of Gaussian fields . Z. Wahrscheinlichkeitstheor. Verwandte. Geb. , 50 : 27 – 52 .
   Web of Science ®Google Scholar
• Taqqu , M. 1975 . Weak convergence to the fractional Brownian motion and to the Rosenblatt process . Z. Wahrscheinlichkeitstheor. Verwandte. Geb. , 31 : 287 – 302 .
   Web of Science ®Google Scholar
• Taqqu , M. 1978 . A representation for self-similar processes . Stoch. Process. Appl. , 7 ( 1 ) : 55 – 64 .
   Google Scholar
• Kleptsyna , M. and Le Breton , A. 2002 . Statistical analysis of the fractional Ornstein-Uhlenbeck process . Stat. Inf. Stoch. Process. , 5 : 229 – 248 .
   Google Scholar
• Tudor , C. A. and Viens , F. 2007 . Statistical aspects of the fractional stochastic calculus . Ann. Stat. , 35 ( 3 ) : 1183 – 1212 .
   Web of Science ®Google Scholar
• Sottinen , T. and Tudor , C. A. 2007 . Parameter estimation for stochastic equations with additive fractional Brownian sheet . Stat. Inf. Stoch. Process. , 11 ( 3 ) : 221 – 236 .
   Google Scholar
• Prakasa Rao , B. L.S. 1999 . Statistical Inference for Diffusion Type Processes , London : Arnold, HodderHeadlone Group .
   Google Scholar
• Torres , S. and Tudor , C. A. 2007 . Donsker type theorem for the Rosenblatt process and a binary market model . Stoch. Anal. Appl. , 27 ( 3 ) : 555 – 573 .
   Web of Science ®Google Scholar
• Golub , G. H. and van Loan , C. F. 1989 . Matrix Computations , Baltimore : Hopkins University Press .
   Google Scholar
• Sottinen , T. 2001 . Fractional Brownian motion, random walks and binary market models . Finance Stoch. , 5 : 343 – 355 .
   Google Scholar
• Duflo , M. 1997 . Random Iterative Models , Berlin : Springer .
   Google Scholar
• Nualart , D. 2003 . Stochastic calculus with respect to the fractional Brownian motion and applications . Contemp. Math. , 336 : 3 – 39 .
   Google Scholar
• Tudor , C. A. 2008 . Analysis of the Rosenblatt process . ESAIM Probab. Stat. , 12 : 230 – 257 .
   Google Scholar