## Semiparametric estimation of fractional cointegrating subspaces.(English)Zbl 1114.62084

Summary: We consider a common-components model for multivariate fractional cointegration, in which the $$s\geq 1$$ 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 $$o_p(1)$$.
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.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M15 Inference from stochastic processes and spectral analysis 62G05 Nonparametric estimation 62H12 Estimation in multivariate analysis 62G20 Asymptotic properties of nonparametric inference

periodogram
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