Asymptotic Normality of Narrow-Band Least Squares in the Stationary Fractional Cointegration Model and Volatility Forecasting

Posted: 28 Jan 2005

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

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 is due to Robinson (1994, Annals of Statistics 22, 515-539) and 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. We derive the asymptotic distribution theory for the FDLS estimator of the cointegration vector in the stationary long memory case, thus complementing Robinson's consistency result. An application to the relation between the volatility realized in the stock market and the associated implicit volatility derived from option prices is offered.

Keywords: Asymptotic distribution theory, high-frequency data, long memory, semiparametric methods, stationary fractional cointegration

JEL Classification: C14, C22, G13

Suggested Citation

Christensen, Bent Jesper and Nielsen, Morten Orregaard, Asymptotic Normality of Narrow-Band Least Squares in the Stationary Fractional Cointegration Model and Volatility Forecasting. Journal of Econometrics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=655444

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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