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December 2006 Semiparametric estimation of fractional cointegrating subspaces
Willa W. Chen, Clifford M. Hurvich
Ann. Statist. 34(6): 2939-2979 (December 2006). DOI: 10.1214/009053606000000894


We consider a common-components model for multivariate fractional cointegration, in which the s≥1 components have different memory parameters. The cointegrating rank may exceed 1. We decompose the true cointegrating vectors into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters. We estimate each cointegrating subspace separately, using appropriate sets of eigenvectors of an averaged periodogram matrix of tapered, differenced observations, based on the first m Fourier frequencies, with m fixed. The angle between the true and estimated cointegrating subspaces is op(1). We use the cointegrating residuals corresponding to an estimated cointegrating vector to obtain a consistent and asymptotically normal estimate of the memory parameter for the given cointegrating subspace, using a univariate Gaussian semiparametric estimator with a bandwidth that tends to ∞ more slowly than n. We use these estimates to test for fractional cointegration and to consistently identify the cointegrating subspaces.


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Willa W. Chen. Clifford M. Hurvich. "Semiparametric estimation of fractional cointegrating subspaces." Ann. Statist. 34 (6) 2939 - 2979, December 2006.


Published: December 2006
First available in Project Euclid: 23 May 2007

zbMATH: 1114.62084
MathSciNet: MR2329474
Digital Object Identifier: 10.1214/009053606000000894

Primary: 62M10
Secondary: 62M15.

Keywords: Fractional cointegration , long memory , periodogram , tapering

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 6 • December 2006
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