ARCH model and fractional Brownian motion

Natalia Bahamonde; Soledad Torres; Ciprian A. Tudor

doi:10.1016/j.spl.2017.10.003

ARCH model and fractional Brownian motion

Natalia Bahamonde, Soledad Torres, Ciprian A. Tudor

INSTITUTE OF STATISTICS

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4 Scopus citations

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.

Original language	English
Pages (from-to)	70-78
Number of pages	9
Journal	Statistics and Probability Letters
Volume	134
DOIs	https://doi.org/10.1016/j.spl.2017.10.003
State	Published - Mar 2018

Keywords

ARCH model
Fractional Brownian motion
Stationary process
Volatility

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10.1016/j.spl.2017.10.003

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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 = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

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doi = "10.1016/j.spl.2017.10.003",

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T1 - ARCH model and fractional Brownian motion

AU - Bahamonde, Natalia

AU - Torres, Soledad

AU - Tudor, Ciprian A.

PY - 2018/3

Y1 - 2018/3

N2 - 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.

AB - 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.

KW - ARCH model

KW - Fractional Brownian motion

KW - Stationary process

KW - Volatility

UR - http://www.scopus.com/inward/record.url?scp=85034628139&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2017.10.003

DO - 10.1016/j.spl.2017.10.003

M3 - Article

AN - SCOPUS:85034628139

SN - 0167-7152

VL - 134

SP - 70

EP - 78

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

ARCH model and fractional Brownian motion

Abstract

Keywords

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