TY - JOUR
T1 - Two-stage stationary bootstrapping for bivariate average realized volatility matrix under market microstructure noise and asynchronicity
AU - Hwang, Eunju
AU - Shin, Dong Wan
N1 - Funding Information:
This paper was greatly indebt by constructive comments of two unknown referees and the editor. This work was supported by the National Research Foundation of Korea ( NRF–2015–1006133 ) and ( NRF-2016–4008780 ).
Publisher Copyright:
© 2017
PY - 2018/2
Y1 - 2018/2
N2 - Under the two important modern financial market features of noise and non-synchronicity for multiple assets, for consistent estimators of the integrated covariations, we adopt the two-time scale average realized volatility matrix (ARVM) which is a matrix extension of the two-time scale realized volatilities of Zhang et al. (2005). An asymptotic normal theory is provided for the two-time scale ARVM and resulting realized covariations. The asymptotic normality is not directly applicable in practice to construct statistical methods owning to nuisance parameters. To bypass the nuisance parameter problem, two-stage stationary bootstrapping is proposed. We establish consistencies of the bootstrap distributions, and construct confidence intervals and hypothesis tests for the integrated covariance, regression coefficient and correlation coefficient. The validity of the stationary bootstrap for the high frequency heterogeneous returns is proved by showing that there exist parameters of the stationary bootstrap blocks so that the bootstrap consistencies hold. The proposed bootstrap methods extend the i.i.d. bootstrapping methods for realized covariations by Dovonon et al. (2013), that are confined to synchronous noise-free sampling. For high frequency noisy asynchronous samples, a Monte-Carlo experiment shows better finite sample performances of the proposed stationary bootstrap methods based on the two-time scale ARVM estimator than the wild blocks of blocks bootstrap methods of Hounyo (2017), based on pre-averaged truncated estimator.
AB - Under the two important modern financial market features of noise and non-synchronicity for multiple assets, for consistent estimators of the integrated covariations, we adopt the two-time scale average realized volatility matrix (ARVM) which is a matrix extension of the two-time scale realized volatilities of Zhang et al. (2005). An asymptotic normal theory is provided for the two-time scale ARVM and resulting realized covariations. The asymptotic normality is not directly applicable in practice to construct statistical methods owning to nuisance parameters. To bypass the nuisance parameter problem, two-stage stationary bootstrapping is proposed. We establish consistencies of the bootstrap distributions, and construct confidence intervals and hypothesis tests for the integrated covariance, regression coefficient and correlation coefficient. The validity of the stationary bootstrap for the high frequency heterogeneous returns is proved by showing that there exist parameters of the stationary bootstrap blocks so that the bootstrap consistencies hold. The proposed bootstrap methods extend the i.i.d. bootstrapping methods for realized covariations by Dovonon et al. (2013), that are confined to synchronous noise-free sampling. For high frequency noisy asynchronous samples, a Monte-Carlo experiment shows better finite sample performances of the proposed stationary bootstrap methods based on the two-time scale ARVM estimator than the wild blocks of blocks bootstrap methods of Hounyo (2017), based on pre-averaged truncated estimator.
KW - High frequency data
KW - Market microstructure noise
KW - Non-synchronous trading
KW - Realized covariations
KW - Stationary bootstrap
KW - Two-time scale estimator
UR - http://www.scopus.com/inward/record.url?scp=85034862916&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2017.10.001
DO - 10.1016/j.jeconom.2017.10.001
M3 - Article
AN - SCOPUS:85034862916
VL - 202
SP - 178
EP - 195
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 2
ER -