Bipower-type estimation in a noisy diffusion setting

Stochastic Processes and their Applications

Volumn 119, Issue 9, 2009, Pages 2803-2831

  Podolskij, Mark ^a   Vetter, Mathias ^b  

^a ETH ZURICH   (Switzerland)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Bipower variation; Central limit theorem; High frequency data; Microstructure noise; Quadratic variation; Semimartingale theory; Test for jumps

Indexed keywords

BIPOWER VARIATION; CENTRAL LIMIT THEOREM; HIGH-FREQUENCY DATA; QUADRATIC VARIATION; SEMIMARTINGALE THEORY; TEST FOR JUMPS;

IMAGE CODING; MICROSTRUCTURE;

ESTIMATION;

EID: 68549109727     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2009.02.006     Document Type: Article

References (23)

1. Andersen T.G., Bollerslev T., Diebold F.X., and Labys P. The distribution of exchange rate volatility. J. Amer. Statist. Assoc. 96 (2001) 42-55
2. Barndorff-Nielsen O.E., and Shephard N. Econometric analysis of realised volatility and its use in estimating stochastic volatility models. J. Roy. Statist. Soc. Ser. B 64 (2002) 253-280
3. J. Jacod, Y. Li, P.A. Mykland, M. Podolskij, M. Vetter, Microstructure noise in the continuous case: The pre-averaging approach. Stochastic Process. Appl. (2007), forthcoming (doi:10.1016/j.spa.2008.11.004)
4. Zhang L., Mykland P.A., and Ait-Sahalia Y. A tale of two time scales: Determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 472 (2005) 1394-1411
5. Zhang L. Efficient estimation of stochastic volatility using noisy observations: a multiscale approach. Bernoulli 12 6 (2004) 1019-1043
6. Barndorff-Nielsen O.E., Hansen P.R., Lunde A., and Shephard N. Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise. Econometrica 76 (2008) 1481-1536
7. M. Podolskij, M. Vetter, Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps. Bernoulli (2007), (forthcoming)
8. Barndorff-Nielsen O.E., Graversen S.E., Jacod J., Podolskij M., and Shephard N. A central limit theorem for realised power and bipower variations of continuous semimartingales. In: Kabanov Y., Lipster R., and Stoyanov J. (Eds). From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift (2006), Springer-Verlag, Berlin 33-68
9. Barndorff-Nielsen O.E., and Shephard N. Power and bipower variation with stochastic volatility and jumps. J. Financ. Econom. 2 (2004) 1-48
10. Ait-Sahalia Y., and Jacod J. Testing for jumps in a discretely observed process. Ann. Statist. 37 1 (2009) 184-222
11. Jacod J., and Shiryaev A.N. Limit Theorems for Stochastic Processes (2003), Springer-Verlag, Berlin
12. Jacod J. Asymptotic properties of realized power variations and related functionals of semimartingales. Stochastic Process. Appl. 118 4 (2008) 517-559
13. J. Jacod, M. Podolskij, M. Vetter, Limit theorems for moving averages of discretized processes plus noise, Tech. Rep., Université de Paris VI, 2008
14. Black F., and Scholes M. The pricing of options and corporate liabilities. J. Polit. Econom. 81 (1973) 637-654
15. Vasicek O.A. An equilibrium characterization of the term structure. J. Financ. Econom. 5 (1977) 177-188
16. Cox J.C., Ingersoll J.E., and Ross S.A. An analysis of variable rate loan contracts. J. Finance 35 (1980) 389-403
17. Chan K.C., Karolyi A.G., Longstaff F.A., and Sanders A.B. An empirical comparison of alternative models of the short-term interest rate. J. Finance 47 (1992) 1209-1227
18. Renyi A. On stable sequences of events. Sankhya Ser. A 25 (1963) 293-302
19. Aldous D.J., and Eagleson G.K. On mixing and stability of limit theorems. Ann. Probab. 6 2 (1978) 325-331
20. Gloter A., and Jacod J. Diffusions with measurement errors. I. Local asymptotic normality. ESAIM Probab. Statist. 5 (2001) 225-242
21. Gloter A., and Jacod J. Diffusions with measurement errors. II. Optimal estimators. ESAIM Probab. Statist. 5 (2001) 243-260
22. J. Jacod, Asymptotic properties of realized power variations and related functionals of semimartingales: Multipower variations, Tech. Rep., Université de Paris VI, 2006
23. Lahiri S.N. Resampling Methods for Dependent Data (2003), Springer-Verlag, Berlin