Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Asymptotics for realized covariance under market microstructure noise and sampling frequency determination

  • Shin, Dong Wan (Department of Statistics, Ewha Womans University) ;
  • Hwang, Eunju (Department of Applied Statistics, Gachon University)
  • Received : 2016.07.22
  • Accepted : 2016.09.02
  • Published : 2016.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Large frequency limiting distributions of two errors in realized covariance are investigated under noisy and non-synchronous high frequency sampling situations. The first distribution characterizes increased variance of the realized covariance due to noise for large frequency and the second distribution characterizes decreased variance of the realized covariance due to discretization for large frequency. The distribution of the combined error enables us to determine the sampling frequency which depends on a nuisance parameter. A consistent estimator of the nuisance parameter is proposed.

Keywords

References

  1. Ait-Sahalia Y, Fan J, and Xiu D (2010). High-frequency covariance estimates with noisy and asynchronous financial data, Journal of the American Statistical Association, 105, 1504-1517. https://doi.org/10.1198/jasa.2010.tm10163
  2. Ait-Sahalia Y, Mykland PA, and Zhang L (2005). How often to sample a continuous-time process in the presence of market microstructure noise, The Review of Financial Studies, 18, 351-416. https://doi.org/10.1093/rfs/hhi016
  3. Bandi FM and Russell JR (2008). Microstructure noise, realized variance, and optimal sampling, The Review of Economic Studies, 75, 339-369. https://doi.org/10.1111/j.1467-937X.2008.00474.x
  4. Barndorff-Nielsen OE and Shephard N (2004). Econometric analysis of realized covariation: high frequency based covariance, regression, and correlation in financial economics, Econometrica, 72, 885-925. https://doi.org/10.1111/j.1468-0262.2004.00515.x
  5. Barndorff-Nielsen OL, Hansen PR, Lunde A, and Shephard N (2011). Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading, Journal of Econometrics, 162, 149-169. https://doi.org/10.1016/j.jeconom.2010.07.009
  6. Bibinger M (2011a). Efficient covariance estimation for asynchronous noisy high-frequency data, Scandinavian Journal of Statistics, 38, 23-45. https://doi.org/10.1111/j.1467-9469.2010.00712.x
  7. Bibinger M (2011b). Asymptotics of asynchronicity (technical report), Retrieved Sep 8, 2016, from: http://sfb649.wiwi.huberlin.de/papers/pdf/SFB649DP2011-033.pdf
  8. Bibinger M (2012). An estimator for the quadratic covariation of asynchronously observed Ito processes with noise: Asymptotic distribution theory, Stochastic Processes and their Applications, 122, 2411-2453. https://doi.org/10.1016/j.spa.2012.04.002
  9. Dovonon P, Goncalves S, and Meddahi N (2013). Bootstrapping realized multivariate volatility measures, Journal of Econometrics, 172, 49-65. https://doi.org/10.1016/j.jeconom.2012.08.003
  10. Griffin JE and Oomen RCA (2011). Covariance measurement in the presence of non-synchronous trading and market microstructure noise, Journal of Econometrics, 160, 58-68. https://doi.org/10.1016/j.jeconom.2010.03.015
  11. Hall P and Heyde CC (1980). Martingale Limit Theory and Its Application, Academic Press, New York.
  12. Hayashi T and Yoshida N (2005). On covariance estimation of non-synchronously observed diffusion processes, Bernoulli, 11,359-379. https://doi.org/10.3150/bj/1116340299
  13. Hwang E and Shin DW (2016). Two-stage stationary bootstrapping for bivariate average realized volatility matrix under market microstructure noise and asynchronicity, Manuscript submitted.
  14. Mykland PA and Zhang L (2002). ANOVA for diffusions (technical report), University of Chicago.
  15. Voev V and Lunde A (2007). Integrated covariance estimation using high-frequency data in the presence of noise, Journal of Financial Econometrics, 5, 68-104.
  16. Zhang L, Mykland PA, and Ait-Sahalia Y (2005). A tale of two time scales: determining integrated volatility with noisy high-frequency data, Journal of the American Statistical Association, 100, 1394-1411. https://doi.org/10.1198/016214505000000169