Inference for continuous semimartingales observed at high frequency

Econometrica

Volumn 77, Issue 5, 2009, Pages 1403-1445

  Mykland, Per A ^a   Zhang, Lan ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Consistency; Contiguity; Continuity; Cumulants; Discrete observation; Efficiency; Equivalent martingale measure; It process; Leverage effect; Likelihood inference; Realized beta; Realized volatility; Stable convergence

Indexed keywords

EID: 70349838736     PISSN: 00129682     EISSN: 14680262     Source Type: Journal    
DOI: 10.3982/ECTA7417     Document Type: Article

References (53)

1. Aït-Sahalia, Y. (2002 Maximum-Likelihood Estimation of Discretely-Sampled Diffusions: A Closed-Form Approximation Approach Econometrica, 70, 223 262.
2. Aldous, D. J., and G. K. Eagleson (1978 On Mixing and Stability of Limit Theorems Annals of Probability, 6, 325 331.
3. Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2001 The Distribution of Realized Exchange Rate Volatility Journal of the American Statistical Association, 96, 42 55.
4. Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2003 Modeling and Forecasting Realized Volatility Econometrica, 71, 579 625.
5. Barndorff-Nielsen, O., S. Graversen, J. Jacod, M. Podolskij, and N. Shephard (2006 A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales in From Stochastic Calculus to Mathematical Finance, The Shiryaev Festschrift, ed. by Y. Kabanov, R. Liptser, and J. Stoyanov. Berlin : Springer Verlag, 33 69.
6. Barndorff-Nielsen, O. E., and N. Shephard (2001 Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics Journal of the Royal Statistical Society, Series B, 63, 167 241.
7. Barndorff-Nielsen, O. E., and N. Shephard (2002 Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models Journal of the Royal Statistical Society, Series B, 64, 253 280.
8. Barndorff-Nielsen, O. E., and N. Shephard (2004 a Econometric Analysis of Realised Covariation: High Frequency Based Covariance, Regression and Correlation in Financial Economics Econometrica, 72, 885 925.
9. Barndorff-Nielsen, O. E., and N. Shephard (2004 b Power and Bipower Variation With Stochastic Volatility and Jumps with discussion Journal of Financial Econometrics, 2, 1 48.
10. Billingsley, P. (1995 Probability and Measure (Third Ed.). New York : Wiley.
11. Chen, Y., and V. Spokoiny (2007 Robust Risk Management. Accounting for Nonstationarity and Heavy Tails Technical Report, Weierstrass Institute, Berlin.
12. Christensen, K., R. Oomen, and M. Podolskij (2008 Realised Quantile-Based Estimation of the Integrated Variance Research Paper 2009-27, CREATES, University of Aarhus, Denmark.
13. Cizek, P., W. Härdle, and V. Spokoiny (2007 Adaptive Pointwise Estimation in Time-Inhomogeneous Time Series Models Technical Report, Weierstrass Institute, Berlin.
14. Comte, F., and E. Renault (1998 Long Memory in Continuous-Time Stochastic Volatility Models Mathematical Finance, 8, 291 323. (Pubitemid 128342547)
15. Dacorogna, M. M., R. Genay, U. Müller, R. B. Olsen, and O. V. Pictet (2001 An Introduction to High-Frequency Finance. San Diego : Academic Press.
16. Dovonon, P., S. Goncalves, and N. Meddahi (2008 Bootstrapping Realized Multivariate Volatility Measures Technical Report, University of Montreal.
17. Duffie, D. (1996 Dynamic Asset Pricing Theory. Princeton, NJ : Princeton University Press.
18. Fan, J., M. Farmen, and I. Gijbels (1998 Local Maximum Likelihood Estimation and Inference Journal of the Royal Statistcal Society, Series B, 60, 591 608.
19. Foster, D., and D. Nelson (1996 Continuous Record Asymptotics for Rolling Sample Variance Estimators Econometrica, 64, 139 174.
20. Hájek, J., and Z. Sidak (1967 Theory of Rank Tests. New York : Academic Press.
21. Hall, P., and C. C. Heyde (1980 Martingale Limit Theory and Its Application. Boston : Academic Press.
22. Harrison, M., and D. Kreps (1979 Martingales and Arbitrage in Multiperiod Securities Markets Journal of Economic Theory, 20, 381 408.
23. Harrison, M., and S. Pliska (1981 Martingales and Stochastic Integrals in the Theory of Continuous Trading Stochastic Processes and Their Applications, 11, 215 260.
24. Hayashi, T., and N. Yoshida (2005 Covariance Estimation of Non-Synchronously Observed Diffusion Processes Bernoulli, 11, 359 379.
25. Heston, S. (1993 A Closed-Form Solution for Options With Stochastic Volatility With Applications to Bonds and Currency Options Review of Financial Studies, 6, 327 343.
26. Jacod, J. (1994 Limit of Random Measures Associated With the Increments of a Brownian Semimartingale Technical Report, Université de Paris VI.
27. Jacod, J. (2008 Asymptotic Properties of Realized Power Variations and Related Functionals of Semimartingales Stochastic Processes and Their Applications 118, 517 559.
28. Jacod, J., and P. Protter (1998 Asymptotic Error Distributions for the Euler Method for Stochastic Differential Equations Annals of Probability, 26, 267 307.
29. Jacod, J., and A. N. Shiryaev (2003 Limit Theorems for Stochastic Processes (Second Ed.). New York : Springer Verlag.
30. Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter (2009 Microstructure Noise in the Continuous Case: The Pre-Averaging Approach Stochastic Processes and Their Applications, 119, 2249 2276.
31. Karatzas, I., and S. E. Shreve (1991 Brownian Motion and Stochastic Calculus (Second Ed.). New York : Springer Verlag.
32. Kinnebrock, S., and M. Podolskij (2008 A Note on the Central Limit Theorem for Bipower Variation of General Functions Stochastic Processes and Their Applications, 118, 1056 1070.
33. LeCam, L. (1986 Asymptotic Methods in Statistical Decision Theory. New York : Springer Verlag.
34. LeCam, L., and G. Yang (2000 Asymptotics in Statistics: Some Basic Concepts (Second Ed.). New York : Springer Verlag.
35. Lehmann, E. (1983 Theory of Point Estimation. New York : Wiley.
36. Mardia, K. V., J. Kent, and J. Bibby (1979 Multivariate Analysis. London : Academic Press.
37. McCullagh, P. (1987 Tensor Methods in Statistics. London : Chapman & Hall.
38. Mykland, P. A. (1993 Asymptotic Expansions for Martingales Annals of Probability, 21, 800 818.
39. Mykland, P. A. (1995 a Embedding and Asymptotic Expansions for Martingales Probability Theory and Related Fields, 103, 475 492.
40. Mykland, P. A. (1995 b Martingale Expansions and Second Order Inference Annals of Statistics, 23, 707 731.
41. Mykland, P. A., and L. Zhang (2006 ANOVA for Diffusions and Itô Processes Annals of Statistics, 34, 1931 1963.
42. Mykland, P. A. (2009 The Econometrics of High Frequency Data in Statistical Methods for Stochastic Differential Equations, ed. by M. Kessler, A. Lindner, and M. Sørensen. New York : Chapman & Hall/CRC Press (forthcoming).
43. Podolskij, M., and M. Vetter (2009 Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps Bernoulli (forthcoming).
44. Renault, E., and B. J. Werker (2009 Causality Effects in Return Volatility Measures With Random Times Journal of Econometrics (forthcoming).
45. Rényi, A. (1963 On Stable Sequences of Events Sanky, Series A, 25, 293 302.
46. Rootzén, H. (1980 Limit Distributions for the Error in Approximations of Stochastic Integrals Annals of Probability, 8, 241 251.
47. Ross, S. M. (1976 The Arbitrage Theory of Capital Asset Pricing Journal of Economic Theory, 13, 341 360.
48. Tibshirani, R., and T. Hastie (1987 Local Likelihood Estimation Journal of the American Statistican Association, 82, 559 567.
49. Weisberg, S. (1985 Applied Linear Regression (Second Ed.). New York : Wiley.
50. Zhang, L. (2001 From Martingales to ANOVA: Implied and Realized Volatility Ph.D. Thesis, Department of Statistics, The University of Chicago.
51. Zhang, L. (2006 Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach Bernoulli, 12, 1019 1043.
52. Zhang, L. (2009 Estimating Covariation: Epps Effect and Microstructure Noise Journal of Economoetrics (forthcoming).
53. Zhang, L., P. A. Mykland, and Y. Aït-Sahalia (2005 A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data Journal of the American Statistical Association, 100, 1394 1411.