The Institute for Statistics and Mathematics is pleased to invite you to the next research seminar, taking place on campus:

Bezirgen Veliyev (Department of Economics and Business Economics, Aarhus University)
Realized Principal Component Analysis of Noisy High-Frequency Data
Wednesday, December 3, 2025, 16:30, in Building D4, Room D4.0.127.

Abstract:
In this paper, we propose a pre-averaging extension of Ait-Sahalia and Xiu (2019), who develop a realized principal component analysis for a continuous-time multi-dimensional log-price process observed discretely over a fixed time interval with vanishing mesh. It applies to study the eigenvalue problem for a time-varying covariance matrix when the high-frequency data are perturbed by measurement error. We derive a consistent noise-robust estimator of the spot covariance in a general framework. Then, exploiting the theory of volatility functional estimation of Jacod and Rosenbaum (2013), we design realized estimators of the integrated eigenvalue, eigenvector and principal component for this setting. We develop a fully-fledged mixed normal distribution theory for the eigenvalue estimator. It presents an asymptotic second-order bias that we show how to correct. In a Monte Carlo study, we document the accuracy of the realized eigenvalue within a standard linear factor model for asset pricing, while an empirical application illuminates its properties on stock market high-frequency data.

Co-authored with Francesco Benvenuti and Kim Christensen.

For further information and the seminar schedule, please see:
www.wu.ac.at/en/statmath/research/resseminar