Testing Collinearity of Vector Time Series

Tucker S. McElroy, Agnieszka Jach

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)


We investigate the collinearity of vector time series in the frequency domain, 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 is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. New asymptotic results for the test statistics are derived under the fixed bandwidth ratio paradigm; they diverge under the alternative, but under the null hypothesis of collinearity the test statistics converge to a non-standard limiting distribution. Subsampling is used to obtain the limiting null quantiles. A simulation study and an empirical illustration for 6-variate time series data are provided.
Original languageEnglish
Peer-reviewed scientific journalThe Econometrics Journal
Issue number2
Pages (from-to)97-116
Number of pages20
Publication statusPublished - 29.01.2019
MoE publication typeA1 Journal article - refereed


  • 512 Business and Management
  • Trend co-integration
  • Seasonal co-integration
  • Schur complement
  • Spectral density rank
  • Fixed-b asymptotics
  • Subsampling


Dive into the research topics of 'Testing Collinearity of Vector Time Series'. Together they form a unique fingerprint.

Cite this