Title: Rank tests for time-varying covariance matrices
Authors: Lars Winkelmann - Freie Universitaet Berlin (Germany) [presenting]
Abstract: The model of a $d$-dimensional continuous-time martingale is considered. The process is observed under observational noise as is standard for microstructure noise models in high-frequency finance. We ask for testing the rank of the time-varying covariance matrix. The test problem is considered locally around some fixed point in time as well as uniformly and in mean over [0, 1]. The signal detection boundary, or optimal separation rate for which the test keeps power under $H_1$, is determined in all three cases. An interesting finding is that this rate does not only depend on the smoothness of the covariance matrix but also significantly on the spectral gap between adjacent eigenvalues. An application to the term structure of interest rates shows the practicability of the new tests.