2018/03/01 by Valeriy Avanesov, Avanesov, Valeriy
Economics, Econometrics and Finance · Mathematics · #62M10 62H15 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1803.00508
openalex publication_date 2018/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The paper proposes a novel testing procedure for this problem. Due to its nature, the approach requires a properly chosen critical level. In this regard we propose a purely data-driven calibration scheme. The approach can be straightforwardly employed in online setting and is essentially multiscale allowing for a trade-off between sensitivity and change-point localization (in online setting, the delay of detection). The description of the algorithm is followed by a formal theoretical study justifying the proposed calibration scheme under mild assumption and providing guaranties for break detection. All the theoretical results are obtained in a high-dimensional setting (dimensionality p >> n). The results are supported by a simulation study inspired by real-world financial data.