Testing for Instability in Covariance Structures
We propose a test for the stability over time of the covariance matrix of multivariate time series. The analysis is extended to the eigensystem to ascertain changes due to instability in the eigenvalues and/or eigenvectors. Using strong Invariance Principle and Law of Large Numbers, we normalize the CUSUM-type statistics to calculate their supremum over the whole sample. The power properties of the test versus local alternatives and alternatives close to the beginning/end of sample are investigated theoretically and via simulation. The testing procedure is validated through an application to 18 US interest rates over 1997-2011, finding instability at the end-2007/beginning-2008. Key Words: Covariance Matrix, Eigensystem, Changepoint, Term Structure of Interest Rates, CUSUM statistic JEL No. C1, C22, C5
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