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 d_k for k=1,...,s. We estimate each cointegrating subsspace 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 coingetraging 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. The angle is O_p(n^{- \alpha_k}), where n is the sample size and \alpha_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 \infty 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.
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Paper provided by EconWPA in its series Econometrics with number
0412007.
Find related papers by JEL classification: C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics C5 - Mathematical and Quantitative Methods - - Econometric Modeling C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
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Carlos Pestana Barros & João Ricardo Faria & Luis A. Gil-Alana, 2008.
"Persistence in Airline Accidents,"
Working Papers
2008/18, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon..
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