Prediction of fractional processes with long-range dependence

被引：0

作者：

Inoue, Akihiko ^{[1
]}

Anh, Vo V. ^{[2
]}

机构：

[1] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan

[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

来源：

HOKKAIDO MATHEMATICAL JOURNAL | 2012年 / 41卷 / 02期

关键词：

Predictor coefficients; prediction; fractional Brownian motion; long-range dependence; BROWNIAN-MOTION; FINANCIAL-MARKETS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H > 1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA(infinity) and AR(infinity) coefficients.

引用

页码：157 / 183

页数：27

共 27 条

[1] Adler R. J., 1981, GEOMETRY RANDOM FIEL
[2] Financial markets with memory II: Innovation processes and expected utility maximization
Anh, V
Inoue, A
Kasahara, Y
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2005, 23 (02) : 301 - 328
[3] Financial markets with memory I: Dynamic models
Anh, V
Inoue, A
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2005, 23 (02) : 275 - 300
[4] Prediction of fractional Brownian motion with Hurst index less than 1/2
Anh, VV
Inoue, A
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2004, 70 (02) : 321 - 328
[5] [Anonymous], 2001, FDN TIME SERIES ANAL
[6] [Anonymous], J APPL MATH STOCHAST
[7] Bingham NH., 1989, REGULAR VARIATION
[8] Stochastic analysis of the fractional Brownian motion
Decreusefond, L
Üstünel, AS
[J]. POTENTIAL ANALYSIS, 1999, 10 (02) : 177 - 214
[9] Duncan T.E., 2002, Stoch. Dyn., V2, P225, DOI [DOI 10.1142/S0219493702000340, 10.1142/S0219493702000340]
[10] A parabolic stochastic differential equation with fractional Brownian motion input
Grecksch, W
Anh, VV
[J]. STATISTICS & PROBABILITY LETTERS, 1999, 41 (04) : 337 - 346

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