Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation

University of Aarhus Working Paper No. 2001-4

34 Pages Posted: 16 Aug 2001

See all articles by Bent Jesper Christensen

Bent Jesper Christensen

Aarhus University; Aarhus University; Aarhus University

Morten Ørregaard Nielsen

Queen's University - Department of Economics

Date Written: August 9, 2002

Abstract

We consider semiparametric frequency domain analysis of cointegration between long memory processes, i.e. fractional cointegration, allowing derivation of useful long-run relations even among stationary processes. The approach uses a degenerating part of the periodogram near the origin to form a narrow band frequency domain least squares (FDLS) estimator of the cointegrating relation, which is consistent for arbitrary short-run dynamics. Our main theoretical contribution is to derive the asymptotic distribution theory for the FDLS estimator of the cointegration vector in the stationary long memory case. The motivating example is the relation between the volatility realized in the stock market and the associated implicit volatility derived from option prices. An application to high-frequency U.S. stock index and option data is offered.

Note: Previously titled Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation in High-Frequency Options Data.

Keywords: Asymptotic distribution theory, Financial options, High-frequency data, Long memory, Long-run relation, Narrow band least squares

JEL Classification: C14, C32, G13

Suggested Citation

Christensen, Bent Jesper and Nielsen, Morten Orregaard, Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation (August 9, 2002). University of Aarhus Working Paper No. 2001-4. Available at SSRN: https://ssrn.com/abstract=279883 or http://dx.doi.org/10.2139/ssrn.279883

Bent Jesper Christensen

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Morten Orregaard Nielsen (Contact Author)

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario
Canada

HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/

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