Inference on the maximal rank of time-varying covariance matrices using high-frequency data

Arbeitspapier

We study the rank of the instantaneous or spot covariance matrix ΣX(t) of a multidimensional continuous semi-martingale X(t). Given highfrequency observations X(i/n), i = 0,...,n, we test the null hypothesis rank (ΣX(t)) <= r for all t against local alternatives where the average (r + 1)st eigenvalue is larger than some signal detection rate vn. A major problem is that the inherent averaging in local covariance statistics produces a bias that distorts the rank statistics. We show that the bias depends on the regularity and a spectral gap of ΣX(t).We establish explicit matrix perturbation and concentration results that provide non-asymptotic uniform critical values and optimal signal detection rates vn. This leads to a rank estimation method via sequential testing. For a class of stochastic volatility models, we determine data-driven critical values via normed p-variations of estimated local covariance matrices. The methods are illustrated by simulations and an application to high-frequency data of U.S. government bonds.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 2021/14

Classification and Topics

• Classification: Wirtschaft
• Subject: empirical covariance matrix ; rank detection ; signal detection rate ; matrix concentration ; eigenvalue perturbation ; principal component analysis ; factor model ; term structure

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Reiß, Markus ; Winkelmann, Lars
• Event: Veröffentlichung
• (who): Freie Universität Berlin, School of Business & Economics
• (where): Berlin
• (when): 2021

Further information

• DOI: doi:10.17169/refubium-32210
• Handle: http://hdl.handle.net/10419/246077
• URN: urn:nbn:de:kobv:188-refubium-32485-6
• Last update: 10.03.2025, 11:45 AM CET