Detecting factors of quadratic variation in the presence of market microstructure noise

A method of detecting latent factors of quadratic variation (QV) of Itô semimartingales from a set of discrete observations is developed when the market microstructure noise is present. We propose a new way to determine the number of latent factors of quadratic co-variations of asset prices based on the SIML (separating information maximum likelihood) method by Kunitomo et al. (Separating information maximum likelihood estimation for high frequency financial data. Springer, Berlin, 2018). In high-frequency financial data, it is important to investigate the effects of possible jumps and market microstructure noise existed in financial markets. We explore the estimated variance–covariance matrix of latent (efficient) prices of the underlying Itô semimartingales and investigate its characteristic roots and vectors of the estimated quadratic variation. We give some simulation results to see the finite sample properties of the proposed method and illustrate an empirical data analysis on the Tokyo stock market.