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How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise

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  • Yacine Ait-Sahalia
  • Per A. Mykland

Abstract

Classical statistics suggest that for inference purposes one should always use as much data as is available. We study how the presence of market microstructure noise in high-frequency financial data can change that result. We show that the optimal sampling frequency at which to estimate the parameters of a discretely sampled continuous-time model can be finite when the observations are contaminated by market microstructure effects. We then address the question of what to do about the presence of the noise. We show that modelling the noise term explicitly restores the first order statistical effect that sampling as often as possible is optimal. But, more surprisingly, we also demonstrate that this is true even if one misspecifies the assumed distribution of the noise term. Not only is it still optimal to sample as often as possible, but the estimator has the same variance as if the noise distribution had been correctly specified, implying that attempts to incorporate the noise into the analysis cannot do more harm than good. Finally, we study the same questions when the observations are sampled at random time intervals, which are an essential feature of transaction-level data.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9611.

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Date of creation: Apr 2003
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Publication status: published as Review of Financial Studies, 2005, vol. 18, pp. 351-416
Handle: RePEc:nbr:nberwo:9611

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  1. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 18(1), pages 83-114, January.
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  3. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  5. Madhavan, Ananth & Richardson, Matthew & Roomans, Mark, 1997. "Why Do Security Prices Change? A Transaction-Level Analysis of NYSE Stocks," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 10(4), pages 1035-64.
  6. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 241-283, January.
  7. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, Econometric Society, vol. 63(4), pages 767-804, July.
  8. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, Elsevier, vol. 8(4), pages 323-361, December.
  9. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers, University of Oxford, Department of Economics 2005-W17, University of Oxford, Department of Economics.
  10. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 1-25, January.
  11. Yacine Ait-Sahalia & Per A. Mykland, 2002. "The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0276, National Bureau of Economic Research, Inc.
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