Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Data

We investigate the computational issues related to the memory size in the estimation of quadratic covariation, taking into account the specifics of financial ultra-high-frequency data. In multivariate price processes, we consider both contamination by the market microstructure noise and the non-synchronicity of the observations. We formulate a multi-scale, flat-top realized kernel, non-flat-top realized kernel, pre-averaging and modulated realized covariance estimators in quadratic form and fix their bandwidth parameter at a constant value. This allows us to operate with limited memory and formulate this estimation as a streaming algorithm. We compare the performance of the estimators with fixed bandwidth parameter in a simulation study. We find that the estimators ensuring positive semidefiniteness require much higher bandwidth than the estimators without this constraint.