A representation theory for a class of vector autoregressive models for fractional processes

Søren Johansen

doi:10.1017/S0266466608080274

A representation theory for a class of vector autoregressive models for fractional processes

Søren Johansen

Økonomisk Institut

107 Citationer (Scopus)

Abstract

Med udgangspunkt i et forslag fra Granger (1986), analyseres en ny vektorautoregressiv model defineret ved hjælp af den fraktionelle lag operator 1-(1-L)^{d}. Først udledes betingelser udtrykt ved koefficienterne for modellen, for at frembringe processer som er fraktionelle af orden nul. Dernæst vises, at hvis der er en enhedsrod, vil modellen frembringe en fraktionel process X(t) af orden d, d>0, for hvilke der er vektorer ß, således at ß'X(t) er fraktionel af orden d-b, 0

Originalsprog	Engelsk
Tidsskrift	Econometric Theory
Vol/bind	24
Udgave nummer	3
Sider (fra-til)	651-676
Antal sider	26
ISSN	0266-4666
DOI	https://doi.org/10.1017/S0266466608080274
Status	Udgivet - 2008

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title = "A representation theory for a class of vector autoregressive models for fractional processes",

abstract = "Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors {\ss} so that {\ss}'X(t) is fractional of order d-b, 0",

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T1 - A representation theory for a class of vector autoregressive models for fractional processes

AU - Johansen, Søren

PY - 2008

Y1 - 2008

N2 - Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0

AB - Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0

KW - Faculty of Social Sciences

U2 - 10.1017/S0266466608080274

DO - 10.1017/S0266466608080274

M3 - Journal article

SN - 0266-4666

VL - 24

SP - 651

EP - 676

JO - Econometric Theory

JF - Econometric Theory

IS - 3

ER -

A representation theory for a class of vector autoregressive models for fractional processes

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