@article{727cd6e3e49244f8947243b5ac825864,
title = "ARCH model and fractional Brownian motion",
abstract = "We study an extension of the ARCH model that includes the squared fractional Brownian motion. We study the statistical properties of the model as the conditions for the existence of a stationary solution and the moments of the process. We study their asymptotic behavior of the autocorrelation function of the squared of the process and we prove that the long memory property of the model holds. We illustrate our results by numerical simulations.",
keywords = "ARCH model, Fractional Brownian motion, Stationary process, Volatility",
author = "Natalia Bahamonde and Soledad Torres and Tudor, {Ciprian A.}",
note = "Funding Information: The authors would like to thank the Editor, an Associate Editor and two anonymous reviewers for valuable comments that led to great improvement of this paper. This research was partially supported by Project ECOS-CONICYT C15E05 , REDES 150038 and MATHAMSUD grant “ 16-MATH-03 SIDRE ” Project. The first author was supported by FONDECYT Grant 1160527 . The second author was supported by FONDECYT Grant 1171335 . The third author was supported by MEC PAI80160046 . Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",
year = "2018",
month = mar,
doi = "10.1016/j.spl.2017.10.003",
language = "English",
volume = "134",
pages = "70--78",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
}