Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation

Morten Ørregaard Nielsen

doi:10.1198/073500106000000314

Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

27 Citationer (Scopus)

Abstract

I consider local Whittle analysis of a stationary fractionally cointegrated model. The local Whittle quasi maximum likelihood estimator is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The proposed estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. I show that the estimator is consistent under weak regularity conditions, and, under an additional local orthogonality condition between the regressors and the cointegration errors, I show asymptotic normality. Indeed, the estimator is asymptotically normal for the entire stationary region of the integration orders, and, thus, for a wider range of integration orders than the narrow-band frequency domain least squares estimator of the cointegration vector, and it is superior to the latter estimator with respect to asymptotic variance. Monte Carlo evidence documenting the finite-sample feasibility of the new methodology is presented. In an application to financial volatility series, I examine the unbiasedness hypothesis in the implied-realized volatility relation.

Originalsprog	Engelsk
Tidsskrift	Journal of Business and Economic Statistics
Vol/bind	25
Nummer	4
Sider (fra-til)	427-446
Antal sider	20
ISSN	0735-0015
DOI	https://doi.org/10.1198/073500106000000314
Status	Udgivet - okt. 2007
Udgivet eksternt	Ja

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title = "Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation",

abstract = "I consider local Whittle analysis of a stationary fractionally cointegrated model. The local Whittle quasi maximum likelihood estimator is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The proposed estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. I show that the estimator is consistent under weak regularity conditions, and, under an additional local orthogonality condition between the regressors and the cointegration errors, I show asymptotic normality. Indeed, the estimator is asymptotically normal for the entire stationary region of the integration orders, and, thus, for a wider range of integration orders than the narrow-band frequency domain least squares estimator of the cointegration vector, and it is superior to the latter estimator with respect to asymptotic variance. Monte Carlo evidence documenting the finite-sample feasibility of the new methodology is presented. In an application to financial volatility series, I examine the unbiasedness hypothesis in the implied-realized volatility relation.",

keywords = "Fractional cointegration, Fractional integration, Long memory, Realized volatility, Semiparametric estimation, Whittle likelihood",

author = "Nielsen, {Morten {\O}rregaard}",

note = "Funding Information: I am grateful to Richard Baillie, Richard Blundell, J{\"o}rg Breitung, Bent Jesper Christensen, Niels Haldrup, Uwe Hassler, Svend Hylleberg, S{\o}ren Johansen, Helmut L{\"u}tkepohl, Neil Shephard, Herman van Dijk, and Tim Vogelsang for many helpful comments and discussions that have significantly improved the article, and to the Danish Social Sciences Research Council (grant FSE 275-05-0220) for financial support. I also thank participants at the 2002 Econometric Society European Meeting in Venice, the 2002 Econometric Society Winter European Meeting in Budapest, the 2002 (EC)2 Conference in Bologna, seminar participants at the University of Aarhus, Tilburg University, University of British Columbia, Cornell University, Michigan State University, and Nuffield College (Oxford), as well as an anonymous associate editor and two anonymous referees for comments. The first version of the article was completed while I was at the University of Aarhus and while visiting Yale University and the Cowles Foundation; their hospitality is gratefully acknowledged.",

year = "2007",

month = oct,

doi = "10.1198/073500106000000314",

language = "English",

volume = "25",

pages = "427--446",

journal = "Journal of Business and Economic Statistics",

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TY - JOUR

T1 - Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation

AU - Nielsen, Morten Ørregaard

N1 - Funding Information: I am grateful to Richard Baillie, Richard Blundell, Jörg Breitung, Bent Jesper Christensen, Niels Haldrup, Uwe Hassler, Svend Hylleberg, Søren Johansen, Helmut Lütkepohl, Neil Shephard, Herman van Dijk, and Tim Vogelsang for many helpful comments and discussions that have significantly improved the article, and to the Danish Social Sciences Research Council (grant FSE 275-05-0220) for financial support. I also thank participants at the 2002 Econometric Society European Meeting in Venice, the 2002 Econometric Society Winter European Meeting in Budapest, the 2002 (EC)2 Conference in Bologna, seminar participants at the University of Aarhus, Tilburg University, University of British Columbia, Cornell University, Michigan State University, and Nuffield College (Oxford), as well as an anonymous associate editor and two anonymous referees for comments. The first version of the article was completed while I was at the University of Aarhus and while visiting Yale University and the Cowles Foundation; their hospitality is gratefully acknowledged.

PY - 2007/10

Y1 - 2007/10

N2 - I consider local Whittle analysis of a stationary fractionally cointegrated model. The local Whittle quasi maximum likelihood estimator is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The proposed estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. I show that the estimator is consistent under weak regularity conditions, and, under an additional local orthogonality condition between the regressors and the cointegration errors, I show asymptotic normality. Indeed, the estimator is asymptotically normal for the entire stationary region of the integration orders, and, thus, for a wider range of integration orders than the narrow-band frequency domain least squares estimator of the cointegration vector, and it is superior to the latter estimator with respect to asymptotic variance. Monte Carlo evidence documenting the finite-sample feasibility of the new methodology is presented. In an application to financial volatility series, I examine the unbiasedness hypothesis in the implied-realized volatility relation.

AB - I consider local Whittle analysis of a stationary fractionally cointegrated model. The local Whittle quasi maximum likelihood estimator is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The proposed estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. I show that the estimator is consistent under weak regularity conditions, and, under an additional local orthogonality condition between the regressors and the cointegration errors, I show asymptotic normality. Indeed, the estimator is asymptotically normal for the entire stationary region of the integration orders, and, thus, for a wider range of integration orders than the narrow-band frequency domain least squares estimator of the cointegration vector, and it is superior to the latter estimator with respect to asymptotic variance. Monte Carlo evidence documenting the finite-sample feasibility of the new methodology is presented. In an application to financial volatility series, I examine the unbiasedness hypothesis in the implied-realized volatility relation.

KW - Fractional cointegration

KW - Fractional integration

KW - Long memory

KW - Realized volatility

KW - Semiparametric estimation

KW - Whittle likelihood

UR - http://www.scopus.com/inward/record.url?scp=35648944166&partnerID=8YFLogxK

U2 - 10.1198/073500106000000314

DO - 10.1198/073500106000000314

M3 - Journal article

AN - SCOPUS:35648944166

SN - 0735-0015

VL - 25

SP - 427

EP - 446

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

IS - 4

ER -

Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation

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