Semiparametric Estimation of Multivariate Fractional
25 Pages Posted: 3 Nov 2008
Date Written: June 2002
We consider the semiparametric estimation of fractional cointegration ina multivariate process of cointegrating rank r > 0. We estimate thecointegrating relationships by the eigenvectors corresponding to the rsmallest eigenvalues of an averaged periodogram matrix of tapered,differenced observations. The number of frequencies m used in theperiodogram average is held fixed as the sample size grows. We firstshow that the averaged periodogram matrix converges in distribution to asingular matrix whose null eigenvectors span the space of cointegratingvectors. We then show that the angle between the estimated cointegratingvectors and the space of true cointegrating vectors is Op(nduôd)where d and du are the memory parameters of the observations andcointegrating errors, respectively. The proposed estimator is invariantto the labeling of the component series, and therefore does not requireone of the variables to be specified as a dependent variable. Wedetermine the rate of convergence of the r smallest eigenvalues of theperiodogram matrix, and present a criterion which allows for consistentestimation of r. Finally, we apply our methodology to the analysis offractional cointegration in interest rates.
Keywords: Fractional cointegration, tapering, periodogram, long memory
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