Semiparametric Estimation of Fractional Cointegrating Subspaces

48 Pages Posted: 3 Nov 2008  

Willa W. Chen

Texas A&M University - Department of Statistics

Clifford M. Hurvich

Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: November 2004

Abstract

We consider a common components model for multivariate fractional cointegration, in which the s ¸ 1 components have different memory parameters. The cointegrating rank is allowed to exceed 1. The true cointegrating vectors can be decomposed into orthogonal fractional cointegrating subspaces suchthat vectors from distinct subspaces yield cointegrating errors with distinct memory parameters, denoted by dk, for k = 1; : : : ; s. We estimate each cointegrating subspace separately using appropriate sets ofeigenvectors of an averaged periodogram matrix of tapered, differenced observations. The averaging uses the first m Fourier frequencies, with m fixed. We will show that any vector in the k th estimatedcointegrating subspace is, with high probability, close to the k th true cointegrating subspace, in the sensethat the angle between the estimated cointegrating vector and the true cointegrating subspace convergesin probability to zero. This angle is Op(n¡®k ), where n is the sample size and ®k is the shortest distance between the memory parameters corresponding to the given and adjacent subspaces. We show that the cointegrating residuals corresponding to an estimated cointegrating vector can be used 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 1 more slowly than n. We also show how these memory parameter estimates can be used to test for fractional cointegration and to consistently identify the cointegrating subspaces.

Keywords: Fractional cointegration, long memory, tapering, periodogram

Suggested Citation

Chen, Willa W. and Hurvich, Clifford M., Semiparametric Estimation of Fractional Cointegrating Subspaces (November 2004). Statistics Working Papers Series, Vol. , pp. -, 2004. Available at SSRN: https://ssrn.com/abstract=1293596

Willa W. Chen (Contact Author)

Texas A&M University - Department of Statistics ( email )

155 Ireland Street
447 Blocker
College Station, TX 77843
United States

Clifford M. Hurvich

Stern School of Business, New York University ( email )

44 West 4th Street
New York, NY 10012-1126
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

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