Limiting spectral distribution of high-dimensional integrated covariance matrices based on high-frequency data with multiple transactions

Abstract

Due to the heavy trading volume in financial markets and the limitations of recording mechanisms, the occurrence of multiple transactions during each recording period is a common feature of high-frequency data. This paper investigates how the number of such multiple transactions impacts the behavior of an averaged version of time-variation adjusted realized covariance (ATVA) matrix in a high-dimensional situation, where the number of stocks and the observation frequency go to infinity proportionally. By using random matrix theory, we derive the limiting spectral distribution (LSD) of ATVA matrices based on high-frequency multiple observations. We demonstrate how the LSD of ATVA matrices depends on the number of multiple transactions. The study of the LSD of random matrices is not only theoretically interesting in itself but also provides a better insight into the pre-averaging approach, which is widely used to deal with the microstructure noise. Furthermore, we investigate the limits of spiked eigenvalues of ATVA matrices when the covariance matrix of asset prices exhibits a spiked pattern. Finally, the theoretical results are supported by simulation studies.