Random aggregation with applications in high-frequency finance

In this paper we consider properties of random aggregation in time series analysis. For application, we focus on the problem of estimating the high-frequency beta of an asset return when the returns are subject to the effects of market microstructure. Specifically, we study the correlation between intraday log returns of two assets. Our investigation starts with the effect of non-synchronous trading on intraday log returns when the underlying return series follows a stationary time series model. This is a random aggregation problem in time series analysis. We also study the effect of non-synchronous trading on the covariance of two asset returns. To overcome the impact of non-synchronous trading, we use Markov chain Monte Carlo methods to recover the underlying log return series based on the observed intraday data. We then define a high-frequency beta based on the recovered log return series and propose an efficient method to estimate the measure. We apply the proposed analysis to many mid-or small-cap stocks using the Trade and Quote Data of the New York Stock Exchange, and discuss implications of the results obtained.