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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/26321
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| Title: | Semiparametric Estimation of Fractional Cointegrating Subspaces |
| Authors: | Chen, Willa W.
Hurvich, Clifford M. |
| Keywords: | Fractional cointegration
long memory
tapering
periodogram |
| Issue Date: | 19-Nov-2004 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | SOR-2004-4 |
| 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 such that 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 of eigenvectors 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 estimated cointegrating subspace is, with high probability,
close to the k’th true cointegrating subspace, in the sense that
the angle between the estimated cointegrating vector and the true
cointegrating subspace converges in 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. |
| URI: | http://hdl.handle.net/2451/26321 |
| Appears in Collections: | IOMS: Statistics Working Papers
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