Covariance matrix analysis for higher order fractional Brownian motion time series

Jean Philippe Montillet; Kegen Yu

doi:10.1109/CCECE.2015.7129488

Covariance matrix analysis for higher order fractional Brownian motion time series

Jean Philippe Montillet, Kegen Yu

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

1 Citation (Scopus)

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.

Your goal is to simulate, as closely as possible, the usual appearance of typeset papers. This document provides an example of the desired layout and contains information regarding desktop publishing format, type sizes, and type faces.

Original language	English
Title of host publication	Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering
Subtitle of host publication	Halifax, Canada, May 3-6, 2015
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	1420-1424
Number of pages	5
ISBN (Electronic)	9781479958290
ISBN (Print)	9781479958276
DOIs	https://doi.org/10.1109/CCECE.2015.7129488
Publication status	Published - 2015
Externally published	Yes
Event	Canadian Conference on Electrical and Computer Engineering (28th : 2015) - Halifax, Canada Duration: 3 May 2015 → 6 May 2015 Conference number: 28th

Publication series

Name
ISSN (Print)	0840-7789

Conference

Conference	Canadian Conference on Electrical and Computer Engineering (28th : 2015)
Country/Territory	Canada
City	Halifax
Period	3/05/15 → 6/05/15

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10.1109/CCECE.2015.7129488

Cite this

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title = "Covariance matrix analysis for higher order fractional Brownian motion time series",

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. Your goal is to simulate, as closely as possible, the usual appearance of typeset papers. This document provides an example of the desired layout and contains information regarding desktop publishing format, type sizes, and type faces.",

author = "Montillet, {Jean Philippe} and Kegen Yu",

year = "2015",

doi = "10.1109/CCECE.2015.7129488",

language = "English",

isbn = "9781479958276",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

pages = "1420--1424",

booktitle = "Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering",

address = "United States",

note = "Canadian Conference on Electrical and Computer Engineering (28th : 2015) ; Conference date: 03-05-2015 Through 06-05-2015",

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Montillet, JP & Yu, K 2015, Covariance matrix analysis for higher order fractional Brownian motion time series. in Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering: Halifax, Canada, May 3-6, 2015. Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 1420-1424, Canadian Conference on Electrical and Computer Engineering (28th : 2015), Halifax, Canada, 3/05/15. https://doi.org/10.1109/CCECE.2015.7129488

Covariance matrix analysis for higher order fractional Brownian motion time series. / Montillet, Jean Philippe; Yu, Kegen.
Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering: Halifax, Canada, May 3-6, 2015. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2015. p. 1420-1424.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - Covariance matrix analysis for higher order fractional Brownian motion time series

AU - Montillet, Jean Philippe

AU - Yu, Kegen

N1 - Conference code: 28th

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N2 - 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. Your goal is to simulate, as closely as possible, the usual appearance of typeset papers. This document provides an example of the desired layout and contains information regarding desktop publishing format, type sizes, and type faces.

AB - 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. Your goal is to simulate, as closely as possible, the usual appearance of typeset papers. This document provides an example of the desired layout and contains information regarding desktop publishing format, type sizes, and type faces.

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EP - 1424

BT - Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering

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T2 - Canadian Conference on Electrical and Computer Engineering (28th : 2015)

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ER -

Covariance matrix analysis for higher order fractional Brownian motion time series

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