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A ROBUST NEIGHBORHOOD TRUNCATION APPROACH TO ESTIMATION OF INTEGRATED QUARTICITY

Published online by Cambridge University Press:  20 August 2013

Torben G. Andersen ,
Dobrislav Dobrev  and
Ernst Schaumburg
Torben G. Andersen*
Affiliation:
Northwestern University
Dobrislav Dobrev
Affiliation:
Federal Reserve Board of Governors
Ernst Schaumburg
Affiliation:
Federal Reserve Bank of New York
*
*Address correspondence to Torben G. Andersen, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, USA;e-mail: t-andersen@northwestern.edu.
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Abstract

We provide a first in-depth look at robust estimation of integrated quarticity (IQ) based on high-frequency data. IQ is the key ingredient enabling inference about volatility and the presence of jumps in financial time series and is thus of considerable interest in applications. We document the significant empirical challenges for IQ estimation posed by commonly encountered data imperfections and set forth three complementary approaches for improving IQ-based inference. First, we show that many common deviations from the jump-diffusive null can be dealt with by a novel filtering scheme that generalizes truncation of individual returns to truncation of arbitrary functionals on return blocks. Second, we propose a new family of efficient robust neighborhood truncation (RNT) estimators for integrated power variation based on order statistics of a set of unbiased local power variation estimators on a block of returns. Third, we find that ratio-based inference, originally proposed in this context by Barndorff-Nielsen and Shephard (2002, Journal of Applied Econometrics 17, 457–477), has desirable robustness properties in the face of regularly occurring data imperfections and thus is well suited for empirical applications. We confirm that the proposed filtering scheme and the RNT estimators perform well in our extensive simulation designs and in an application to the individual Dow Jones 30 stocks.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 1 , February 2014 , pp. 3 - 59
Copyright
Copyright © Cambridge University Press 2013 

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References

REFERENCES

Andersen, T.G. & Bollerslev, T. (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review 39, 885–905.CrossRefGoogle Scholar
Andersen, T.G., Bollerslev, T., & Diebold, F.X. (2007) Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. Review of Economics and Statistics 89, 701–720.CrossRefGoogle Scholar
Andersen, T.G., Bollerslev, T., & Diebold, F.X. (2010) Parametric and nonparametric volatility measurement, North Holland, In Aït-Sahalia, Y., Hansen, L.P., & Scheinkman, J. A. (eds.). Handbook of Financial Econometrics, Vol. 1. Tools and Techniques.Google Scholar
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, 42–55.CrossRefGoogle Scholar
Andersen, T.G., Bollerslev, T., Diebold, F.X., & Labys, P. (2003) Modeling and forecasting realized volatility. Econometrica 71, 579–625.CrossRefGoogle Scholar
Andersen, T.G., Bollerslev, T., & Dobrev, D. (2007): No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: theory and testable distributional implications. Journal of Econometrics 138, 125–180.CrossRefGoogle Scholar
Andersen, T.G., Dobrev, D.P., & Schaumburg, E. (2008) Duration Based Volatility Estimation. Manuscript, Northwestern University.Google Scholar
Andersen, T.G., Dobrev, D.P., & Schaumburg, E. (2011) A Functional Filtering and Neighborhood Truncation Approach to Integrated Quarticity Estimation NBER Working paper 17152.CrossRefGoogle Scholar
Andersen, T.G., Dobrev, D.P., & Schaumburg, E. (2012) Jump-robust volatility estimation using nearest neighbor truncation Journal of Econometrics 169, 75–93.CrossRefGoogle Scholar
Back, K. (1991) Asset pricing for general processes. Journal of Mathematical Economics 20, 371–395.CrossRefGoogle Scholar
Bandi, F.M. & Russell, J.R. (2008) Microstructure noise, realized variance, and optimal sampling. Review of Economic Studies 75, 339–369.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E., Graversen, S.E., Jacod, J., Podolskij, M., & Shephard, N. (2006) A central limit theorem for realized power and bipower variations of continuous semimartingales. In Kabanov, Yu, Liptser, R., Stoyanov, S. J. (eds.), From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift. Springer Verlag.Google Scholar
Barndorff-Nielsen, O.E., Graversen, S.E., Jacod, J., & Shephard, N. (2006) Limit theorems for Bipower variation in financial econometrics. Econometric Theory, 22, 677–719.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E., Hansen, P.R., Lunde, A., & Shephard, N. (2008) Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica,76, 1481–1536.Google Scholar
Barndorff-Nielsen, O.E., Hansen, P.R., Lunde, A., & Shephard, N. (2009) Realised kernels in practice: Trades and quotes. Econometrics Journal 12, C1–C32.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E. & Shephard, N. (2002) Estimating quadratic variation using realized variance. Journal of Applied Econometrics 17, 457–477.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E. & Shephard, N. (2004a) Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica 72, 885–925.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E. & Shephard, N. (2004b) Power and bipower variation with stochastic volatility and Jumps. Journal of Financial Econometrics 2, 1–37.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E. & Shephard, N. (2006) Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics 4, 1–30.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E., Shephard, N., & Winkel, M. (2006) Limit theorems for multipower variation in the presence of jumps. Stochastic processes and their applications 116, 796–806.CrossRefGoogle Scholar
Christensen, K., Oomen, R., & Podolskij, M. (2008) Realized Quantile-Based Estimation of Integrated Variance. Working paper; CREATES, University of Aarhus.CrossRefGoogle Scholar
Christensen, K., Oomen, R., & Podolskij, M. (2010) Realized quantile-based estimation of integrated variance. Journal of Econometrics 159, 74–98.CrossRefGoogle Scholar
Corsi, F., Pirino, D., & Ren, R. (2010) Threshold bipower variation and the impact of jumps on volatility forecasting. Journal of Econometrics 159, 276–288.CrossRefGoogle Scholar
Hasbrouck, J. (1999) The dynamics of discrete bid and ask quotes. Journal of Finance 54, 2109–2142.CrossRefGoogle Scholar
Hautsch, N. & Podolskij, M. (2013) Pre-averaging based estimation of quadratic variation in the presence of noise and jumps: Theory, implementation, and empirical evidence. Journal of Business and Economic Statistics 31, 165–183.CrossRefGoogle Scholar
Hsieh, D.A. (1991) Chaos and nonlinear dynamics: Applications to financial markets. Journal of Finance 46, 1839–1878.CrossRefGoogle Scholar
Huang, X. & Tauchen, G. (2005) The relative contribution of jumps to total price variance. Journal of Financial Econometrics 3, 456–499.CrossRefGoogle Scholar
Jacod, J., Li, Y., Mykland, P., Podolskij, M., & Vetter, M. (2009) Mirostructure noise in the continuous case: The pre-averaging approach. Stochastic Processes and Their Applications 26, 2803–2831.Google Scholar
Jacod, J. & Protter, P. (1998) Asymptotic error distributions for the Euler method for stochastic differential equations. Annals of Probability 26, 267–307.CrossRefGoogle Scholar
Jacod, J. & Shiryaev, A.N. (2003) Limit Theorems for Stochastic Processes (2nd ed.). Grundlehren der mathematischen Wissenschaften. Springer.CrossRefGoogle Scholar
Jiang, G.J. & Oomen, R.C. (2008) Testing for jumps when asset prices are observed with noise - a “swap variance” approach. Journal of Econometrics 144, 352–370.CrossRefGoogle Scholar
Mancini, C. (2009) Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps. Scandinavian Journal of Statistics 36, 270–296.CrossRefGoogle Scholar
Mykland, P.A. & Zhang, L. (2009) Inference for continuous semimartingales observed at high frequency. Econometrica 77, 1403–1445.Google Scholar
Podolskij, M. & Vetter, M. (2009a) Bipower-type estimation in a noisy diffusion setting. Stochastic Processes and Their Applications 119, 2803–2831.CrossRefGoogle Scholar
Podolskij, M. & Vetter, M. (2009b) Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps. Bernoulli 15, 634–658.CrossRefGoogle Scholar
Revuz, D. & Yor, M. (1999) Continuous Martingales and Brownian Motion (3rd ed.). Grundlehren der mathematischen Wissenschaften. Springer.CrossRefGoogle Scholar
Schwert, G.W. (1989) Why does stock market volatility change over time? The Journal of Finance 44, 1115–1153.CrossRefGoogle Scholar
Zhang, L., Mykland, P.A., & Aït-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.CrossRefGoogle Scholar
Zhou, B. (1996) High-frequency data and volatility in foreign-exchange rates. Journal of Business and Economic Statistics 14, 45–52.Google Scholar