Covariance matrix analysis for higher order fractional Brownian motion time series

Jean Philippe Montillet, Kegen Yu

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

Abstract

Fractional Brownian motion (fBm) is an important mathematical model for describing a range of phenomena and processes. The properties of discrete time fBm (dfBm) when m equals 1 and 2 have been reported in the literature. This paper focuses on analysis of auto-covariance matrix of the m-th order (m > 2) of a dfBm process and the error associated with the approximation of a large dimensional auto-covariance matrix. Applying matrix theory and analysis, we also generalize the asymptotic properties of the eigenvalues of the auto-covariance matrix. Based on the analysis, two theorems and one lemma are proposed and their proofs are provided.

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Original languageEnglish
Title of host publicationProceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering
Subtitle of host publicationHalifax, Canada, May 3-6, 2015
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages1420-1424
Number of pages5
ISBN (Electronic)9781479958290
ISBN (Print)9781479958276
DOIs
Publication statusPublished - 2015
Externally publishedYes
EventCanadian Conference on Electrical and Computer Engineering (28th : 2015) - Halifax, Canada
Duration: 3 May 20156 May 2015
Conference number: 28th

Publication series

Name
ISSN (Print)0840-7789

Conference

ConferenceCanadian Conference on Electrical and Computer Engineering (28th : 2015)
CountryCanada
CityHalifax
Period3/05/156/05/15

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