## The Annals of Statistics

### Semiparametric estimation of fractional cointegrating subspaces

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 34, Number 6 (2006), 2939-2979.

Dates
First available in Project Euclid: 23 May 2007

https://projecteuclid.org/euclid.aos/1179935071

Digital Object Identifier
doi:10.1214/009053606000000894

Mathematical Reviews number (MathSciNet)
MR2329474

Zentralblatt MATH identifier
1114.62084

Subjects
Secondary: 62M15.

#### Citation

Chen, Willa W.; Hurvich, Clifford M. Semiparametric estimation of fractional cointegrating subspaces. Ann. Statist. 34 (2006), no. 6, 2939--2979. doi:10.1214/009053606000000894. https://projecteuclid.org/euclid.aos/1179935071

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