2006/12/01 by Willa W. Chen, Clifford M. Hurvich · 10 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Cointegration #Combinatorics #Eigenvalues and eigenvectors #Estimator #Linear subspace #Mathematical analysis #Mathematics #Multivariate statistics #Probabilistic and Robust Engineering Design #Pure mathematics #Rank (graph theory) #Statistical Distribution Estimation and Applications #Statistics #Subspace topology #Univariate #math.ST #msc:62M10 #msc:62M15. #stat.TH
paper · pdf · doi:10.1214/009053606000000894
published in The Annals of Statistics 34(6) (Institute of Mathematical Statistics) · Published at http://dx.doi.org/10.1214/009053606000000894 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/12/01 · arxiv created 2007/08/01 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.