Semiparametric estimation of fractional cointegrating subspaces

TL;DR

This paper introduces a method for estimating and testing fractional cointegrating subspaces in multivariate time series with different memory parameters, improving understanding of their structure and properties.

Contribution

It proposes a novel approach to decompose and estimate fractional cointegrating subspaces using eigenvector analysis of periodogram matrices, with asymptotic properties and testing procedures.

Findings

Consistent estimation of cointegrating subspaces.

Asymptotic normality of memory parameter estimates.

Effective testing for fractional cointegration.

Abstract

We consider a common-components model for multivariate fractional cointegration, in which the $s\geq1$ 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 $o_p(1)$. 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 $\infty$ more slowly than $n$. We use these estimates to test for fractional cointegration and to consistently identify the cointegrating subspaces.