Performance of estimators of quadratic variation based on high frequency data—empirical review
https://doi.org/10.25205/2542-0429-2020-20-3-47-69
Abstract
Recently, advances in computer technology and data recording and storage have made high-frequency financial data readily available to researchers. As a result, the volatility literature has steadily progressed toward the use of higher-frequency data. However, the move towards the use of higher-frequency financial data in the estimation of volatility of financial returns has resulted in the development of many realised volatility measures of asset return variability based on a variety of different assumptions and functional forms and thus making theoretical comparison and selection of the estimators for empirical applications very difficult if not impossible. This article provides an empirical review on the performance of estimators of quadratic variation/integrated variance based on high-frequency data to aid their application in empirical analysis. The result of the review shows that no single estimator works best in all situations; however, the more sophisticated realised measures, in particular the TSRV and KRV, are superior to the other estimators in terms of their estimation accuracy in the presence of market microstructure noise.
About the Authors
J. Gayomey
Novosibirsk State University (Novosibirsk, Russian Federation)
Russian Federation
Russian Federation
Graduate Studen
A. Kostin
Institute of Economics
and Industrial Engineering of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk State
University (Novosibirsk, Russian Federation)
Russian Federation
Russian Federation
Candidate of Economics, Senior Researcher, Associate Professor,
References
1. Andersen T.G., Bollerslev T., Diebold F.X., Labys P., (2000). Understanding, Optimizing, Using and Forecasting) Realized Volatility and Correlation. Great Realizations," Risk, 105-108.
2. Aït-Sahalia Y., Yu J. (2009). High Frequency Market Microstructure Noise Estimates and Liquidity Measures. The Annals of Applied Statistics, Vol. 3, No. 1, 422–457. DOI: 10.1214/08-AOAS200
3. Sizova N. (2011). Integrated variance forecasting: Model based vs. reduced form. Journal of Econometrics, Volume 162, Issue 2, Pages 294-311
4. Andersen T.G., Bollerslev T., Diebold F.X., Labys P. (2001). The Distribution of Realized Exchange Rate Volatility, Journal of the American Statistical Association, 96:453, 42-55, DOI: 10.1198/016214501750332965
5. Andersen T.G., Bollerslev T., Diebold X.F., Labys P. (2003). Modeling and Forecasting Realized Volatility. Econometrica, Vol. 71, No. 2, 579–625
6. Barndorff‐Nielsen O.E., Shephard N. (2002a). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, Volume17, Issue5, Pages 457-477
7. Pigorsch C., Pigorsch U., Popov I. (2012) Volatility Estimation Based on High-Frequency Data. In: Duan JC., Härdle W., Gentle J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg
8. Barndor-Nielsen and Shephard (2002b) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society Series B, 2002, vol. 64, issue 2, 253-280.
9. Zhang L., Mykland P.A., Aït-Sahalia. Y. (2005). Tale of Two Time Scales. Journal of the American Statistical Association, 100:472, 1394-1411, DOI: 10.1198/016214505000000169
10. McAleer M.,Medeiros M. C.(2008). Realized Volatility: A Review; Econometric Reviews, 27(1–3):10–45
11. Liu L. Y., Patton A. J., Sheppard K. Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes. Journal of Econometrics, 2015, Volume 187, Issue 1, Pages 293-311
12. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine. Edgeworth expansions for realized volatility and related estimators. Journal of Econometrics, 2011, vol. 160(1), p. 190-203.
13. Zhang L. Efficient estimation of stochastic volatility using noisy observations: a multi-scale approach. Bernoulli, 2006, 12(6), 1019–1043
14. Zhou Bin High-Frequency Data and Volatility in Foreign-Exchange Rates. Journal of Business & Economic Statistics, 1996, vol. 14, issue 1, 45-52
15. Hansen P.R., Lunde A. Realized Variance and Market Microstructure Noise. Journal of Business & Economic Statistics, 2006, 24:2, 127-161, DOI: 10.1198/073500106000000071
16. Barndor-Nielsen, Hansen, Lunde, and Shephard Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise. Econometrica, 2008, vol. 76, issue 6, 1481-1536
17. Barndorff‐Nielsen O.E., Hansen P.R., Lunde A., Shephard N. Realized kernels in practice: trades and quotes. The Econometrics Journal, 2009, Volume 12, Issue 3, Pages C1–C32. URL:
18. Christensen K., Podolskij M. Realized range-based estimation of integrated variance.Journal of Econometrics, 2007, Volume 141, Issue 2, Pages 323-349
19. Martens M., Dijk D.. Measuring volatility with the realized range. Journal of Econometrics, 2007, Volume 138, Issue 1, Pages 181-207
20. Christensen K., Podolskij M.,Vetter M. Bias-correcting the realized range-based variance in the presence of market microstructure noise. Finance and Stochastics, 2009, Volume 13, Issue 2, pp 239–268
21. Pearson, G. A. Factors controlling the distribution of forest types, Part I. Ecology, Volume 1, 1920, pp.139-154.
22. Mosteller, F.. On some useful "inefficient" statistics. Annals of Mathematical Statistics, 17, 1946, pp. 377–408
23. Isidore Eisenberger and Edward C. Posner Systematic Statistics Used for Data Compression in Space Telemetry. Journal of the American Statistical Association, Vol. 60, No. 309 (Mar., 1965), pp. 97-133
24. Christensen, Kim and Oomen, Roel C.A. and Podolskij, Mark, Realised Quantile-Based Estimation of the Integrated Variance (September 1, 2009). Journal of Econometrics, Vol 159, No. 1, pp. 74-98, 2010. Available at SSRN: https://ssrn.com/abstract=1085553
25. D. Cho, R. Frees Estimating the volatility of discrete stock prices. Journal of Finance, 43, 1988, pp. 451-466.
26. Andersen T. G., Dobrev, D., Schaumburg E. (2009). Duration-Based Volatility Estimation. URL:
27. Bollerslev T., Kretschmer U., Pigorsch C.,Tauchen G. (2009).A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects. Journal of Econometrics, Volume 150, Issue 2, Pages 151-166
28. Huang X., Tauchen G., (2005). The Relative Contribution of Jumps to Total Price Variance. Journal of Financial Econometrics, Volume 3, Issue 4, Pages 456–499, URL:
29. Carlston B. (2017). Data-Based Ranking of Integrated Variance Estimators Across Size Deciles. Journal of Economic Theory and Econometrics, Vol. 28, No. 1, 21–48
30. Mancini, C. Disentangling the jumps of the diffusion in a geometric jumping Brownian motion. G. dell. Ital. degli Attuari 64, 19–47, 2001.
31. Mancini, C. Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps. Scand. J. Stat. 36 (2), 270–296, 2009.
32. Patton A. J. (2011). Data-based ranking of realised volatility estimators. Journal of Econometrics, Volume 161, Issue 2, Pages 284-303
33. Romano, J.P., Wolf, M. Stepwise multiple testing as formalized data snooping. Econometrica 73 (4), 1237–1282, 2005.
34. Diebold, F.X., Mariano, R.S.. Comparing predictive accuracy. Journal of Business and Economic Statistics 13, 253–263, 1995.
35. Bandi, F.M., Russell, J.R., 2006. Separating microstructure noise from volatility. Journal of Financial Economics 79, 655-692.
36. Bandi, F.M., Russell, J.R., Zhu, Y., (2008). Using high-frequency data in dynamic portfolio choice. Econometric Reviews 27, 163_198
37. Ghysels, E., Sinko, A., 2006. Comment on Hansen and Lunde. Journal of Business and Economic Statistics 24, 192_194.
38. Large J, 2006. Estimating quadratic variation when quoted prices change by constant increments. Working Paper.
39. Large J.(2011).Estimating quadratic variation when quoted prices change by a constant increment; Journal of Econometrics; Volume 160, Issue 1, January 2011, Pages 2-11
40. Aït-Sahalia, Y., Mancini, L., (2008). Out-of-sample forecasts of quadratic variation. Journal of Econometrics 147 (1), 17_33.
41. Andersen, T.G., Bollerslev, T., Meddahi, N., 2006. Realized volatility forecasting and market microstructure noise. Working Paper.
42. Ghysels, E., Sinko, A., 2006b. Volatility forecasting and microstructure noise. Working Paper.
43. Bandi, F.M., Russell, J.R., 2005. Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations. Working Paper.
44. Bandi, F.M., Russell, J.R., 2006. Separating microstructure noise from volatility. Journal of Financial Economics 79, 655_692.
45. Bandi, F.M., Russell, J.R., (2008). Volatility. In: Birge, J., Linetski, V. (Eds.), Handbook of Financial Engineering. Elsevier, North Holland.
46. De Pooter, M., Martens, M., Van Dijk, D., (2008). Predicting the daily covariance matrix for S&P100 stocks using intraday data: But which frequency to use? Econometric Reviews 27, 199_229.
47. Bandi, F.M., Russell, J.R., (2008). Microstructure noise, realized variance, and optimal sampling. Review of Economic Studies 75, 339_369.
48. Bandi F. M_, Jeffrey R. Russell J. R. and Yang C. (2008). Realized volatility forecasting and option pricing. Journal of Econometrics 147, 34-46
Review
For citations:
Gayomey J., Kostin A. Performance of estimators of quadratic variation based on high frequency data—empirical review. World of Economics and Management. 2020;20(3):47-69. (In Russ.) https://doi.org/10.25205/2542-0429-2020-20-3-47-69
Views:
198
Email this article 
