Estimation of [formula omitted], [formula omitted] and portfolio weights in a pure-jump model with long memory in volatility

Abstract

We investigate a bivariate pure-jump model of stock prices with long memory in volatility, using a marked log-Gaussian Cox process. We show that, due to the non-synchronicity of transactions, the ordinary least squares estimator of the slope in a contemporaneous regression of returns on returns converges to different targets depending on the sampling frequency. Therefore, we propose a transaction-level estimator that makes full use of data in the complete continuous-time record, and show that the estimator of the slope has slow convergence with rate determined by the memory parameter in volatility.