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ERROR ASSESSMENT IN MODELING WITH FRACTAL BROWNIAN MOTIONS
Qiao, Bingqiang; Liu, Siming
2013-09-01
Source PublicationFRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume21Issue:3-4
AbstractTo model a given time series F(t) with fractal Brownian motions (fBms), it is necessary to have appropriate error assessment for related quantities. Usually the fractal dimension D is derived from the Hurst exponent H via the relation D = 2-H, and the Hurst exponent can be evaluated by analyzing the dependence of the rescaled range on the time span tau. For fBms, the error of the rescaled range not only depends on data sampling but also varies with H due to the presence of long term memory. This error for a given time series then can not be assessed without knowing the fractal dimension. We carry out extensive numerical simulations to explore the error of rescaled range of fBms and find that for 0 < H < 0.5, vertical bar F(t + tau) - F(t)vertical bar can be treated as independent for time spans without overlap; for 0.5 < H < 1, the long term memory makes vertical bar F(t + tau) - F(t)vertical bar correlated and an approximate method is given to evaluate the error of . The error and fractal dimension can then be determined self-consistently in the modeling of a time series with fBms.
KeywordFractal Brownian Motion Error Assessment Hurst Exponent Standard Deviation Time Series
WOS HeadingsScience & Technology ; Physical Sciences
DOI10.1142/S0218348X13500187
Indexed BySCI
Language英语
WOS Research AreaMathematics ; Science & Technology - Other Topics
WOS SubjectMathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS IDWOS:000329403700004
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://libir.pmo.ac.cn/handle/332002/15512
Collection暗物质和空间天文实验室
AffiliationChinese Acad Sci, Key Lab Dark Matter & Space Astron, Purple Mt Observ, Nanjing 210008, Jiangsu, Peoples R China
Recommended Citation
GB/T 7714
Qiao, Bingqiang,Liu, Siming. ERROR ASSESSMENT IN MODELING WITH FRACTAL BROWNIAN MOTIONS[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,2013,21(3-4).
APA Qiao, Bingqiang,&Liu, Siming.(2013).ERROR ASSESSMENT IN MODELING WITH FRACTAL BROWNIAN MOTIONS.FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,21(3-4).
MLA Qiao, Bingqiang,et al."ERROR ASSESSMENT IN MODELING WITH FRACTAL BROWNIAN MOTIONS".FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 21.3-4(2013).
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