Realized regression with asynchronous and noisy high frequency and high dimensional data

Abstract

We develop regression for high frequency data. This regression is novel in that it can be for both fixed and increasing dimension. Also, the data may have microstructure noise, and observations (trades, or quotes) can be asynchronous, (i.e., the observations do not need to be synchronized across dimensions). As is customary for high-frequency inference methods, we refer to our method as “realized” regression.In our methodology, spot beta becomes a key quantity in the nonparametric framework of high frequency econometrics. The central contribution of this paper is a feasible estimator of spot beta, which is robust to noise and asynchronicity. With the help of the spot-version of the Smoothed TSRV estimator, spot beta can be consistently estimated. There are two direct applications of the spot beta estimates in the current paper. In the first application, the integrated beta can be consistently estimated by aggregating the spot beta estimates. After a bias-correction procedure, a fixed dimension central limit theorem is established for the bias-corrected estimator, with convergence rate which may be arbitrarily close to Op(n−1/4). In the second application we assume time-varying factor structure and conditional sparsity. The spot beta matrix estimator enables the estimation of high dimensional spot covariance and precision matrices. The latter is obtained by thresholding the spot residual covariance estimates, and convergence rates derived. As an empirical application, this paper explores the hourly change in beta around earnings announcements of the S&P 100 constituents.