Estimation of Integrated Covariances in the Simultaneous Presence of Nonsynchronicity, Microstructure Noise and Jumps

Abstract

We propose a new estimator for the integrated covariance of two Itô semimartingales observed at a highfrequency. This new estimator, which we call the pre-averaged truncated Hayashi-Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in the case that the sampling schemes of two processes are nonsynchronous and the observation data is polluted by some noise. It is the first estimator which can simultaneously handle these three issues, which are fundamental to empirical studies of high-frequency financial data. We also show the asymptotic mixed normality of this estimator under some mild conditions allowing infinite activity jump processes with finite variations, some dependency between the sampling times and the observed processes as well as a kind of endogenous observation errors. We examine the finite sample performance of this estimator using a Monte Carlo study.

Common price and volatility jumps in noisy high-frequency data

“…Different to Assumption (GN) in Section 7.2 of Aït-Sahalia and Jacod (2014), we do not assume that the noise is conditionally centered to include the correlation to the increments of X in (23). The endogeneity condition (23) includes linear models of the form i = i l=i−Q c l √ n∆ n l X + U i , with U i exogenous errors and constants c l , similar as in Equation (6) of Koike (2016) or considered by Barndorff-Nielsen et al (2008). If we knew the process (η t ) t∈[0,1] , Assumption (η-p) with a mild lower bound for would be sufficient for our asymptotic results.…”

Bayesian Analysis of Realized Matrix-Exponential GARCH Models

“…Three stocks traded on the New York Stock Exchange are selected, namely: Bank of America (BAC), General Electric (GE), and International Business Machines (IBM). Based on the vector of returns for the m = 3 stocks computed for a 1-minute interval of trading day at t between 9:30 am and 4:00 pm, we calculated the daily values of the estimates of integrated co-volatility matrix, via the approach of Koike (2016). The estimator of Koike (2016) is robust to jumps and microstructure noise, and has an ability to handle asynchronicity of the times at which transactions are recorded.…”

“…Based on the vector of returns for the m = 3 stocks computed for a 1-minute interval of trading day at t between 9:30 am and 4:00 pm, we calculated the daily values of the estimates of integrated co-volatility matrix, via the approach of Koike (2016). The estimator of Koike (2016) is robust to jumps and microstructure noise, and has an ability to handle asynchronicity of the times at which transactions are recorded. As in Asai and McAleer (2017), we modify the estimator of Koike (2016) to guarantee the positive definiteness of the covariance matrix, by the threshold method of Bickel and Levina (2008).…”

“…The estimator of Koike (2016) is robust to jumps and microstructure noise, and has an ability to handle asynchronicity of the times at which transactions are recorded. As in Asai and McAleer (2017), we modify the estimator of Koike (2016) to guarantee the positive definiteness of the covariance matrix, by the threshold method of Bickel and Levina (2008). We denote the estimate of integrated co-volatility matrix at dat t as C t , giving X t = Log(C t ).…”

Confidence interval for correlation estimator between latent processes

“…This modeling was successful and denoising techniques have also been developed: sub-sampling (Zhang et al [48], Zhang [49]), pre-averaging (Podolskij and Vetter [43], Jacod et al [25]), and others (Zhou [50]). There are many studies that treat both non-synchoronicity and market microstructure noise: Malliavin and Mancino [34], Mancino and Sanfelici [35], Park and Linton [42], Voev and Lunde [47], Griffin and Oomen [19], Christensen et al [12,13], Koike [27,29,28], Aït-Sahalia et al [4], Barndorff-Nielsen et al [6], Bibinger [8,9].…”