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Title: Testing collinearity of vector time series Authors:  Agnieszka Jach - Hanken School of Economics (Finland) [presenting]
Tucker McElroy - Census Bureau (United States)
Abstract: The collinearity of vector time series in the frequency domain is investigated by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series data is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We pursue a full understanding of rank through the Schur complements of the spectral density matrix, and test for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. We provide new asymptotic results for the Schur complements, under the fixed bandwidth ratio paradigm. The test statistics are $O_P(1)$ under the alternative, but under the null hypothesis of collinearity the test statistics are $O_P(T^{-1})$, and the limiting distribution is non-standard. Subsampling is used to obtain the limiting null quantiles. Simulation study and an empirical illustration for six-variate time series data are provided.