Title: A shrinkage estimator of quadratic variation in high-dimensional settings
Authors: Kim Christensen - Aarhus University (Denmark)
Mikkel Slot Nielsen - Columbia University (United States) [presenting]
Mark Podolskij - University of Luxembourg (Luxembourg)
Abstract: An estimator of the quadratic variation of high-dimensional semimartingales is proposed based on nuclear-norm penalization. Specifically, under suitable conditions, we prove a concentration inequality for estimators obtained by soft-thresholding of the eigenvalues of the realized variance. By relying on this result, we show that, by proper tuning, one can obtain an estimator of the quadratic variation which is minimax optimal up to a logarithmic factor and has the true rank with high probability. The theory is extended to include estimation of the local volatility and it is complemented by a simulation study as well as an empirical application.