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RFS Advance Access published online on February 10, 2005
Review of Financial Studies, doi:10.1093/rfs/hhi016
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The Review of Financial Studies © The Author 2005. Published by Oxford University Press on behalf of the Society of for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

Original Articles

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

Yacine Aït-Sahalia 1*, Per A. Mykland 2, and Lan Zhang 3
1 Princeton University and NBER
2 The University of Chicago
3 Carnegie Mellon University

* To whom correspondence should be addressed.
Yacine Aït-Sahalia, E-mail: yacine{at}princeton.edu


  Abstract

In theory, the sum of squares of log returns sampled at high frequency estimates their variance. When market microstructure noise is present but unaccounted for, however, we show that the optimal sampling frequency is finite and derive its closed-form expression. But even with optimal sampling, using say five minute returns when transactions are recorded every second, a vast amount of data is discarded, in contradiction to basic statistical principles. We demonstrate that modelling the noise and using all the data is a better solution, even if one misspecifies the noise distribution. So the answer is: sample as often as possible.

*We are grateful for comments and suggestions from the editor, Maureen O'Hara, and two anonymous referees, as well as seminar participants at Berkeley, Harvard, NYU, MIT, Stanford, the Econometric Society and the Joint Statistical Meetings. Financial support from the NSF under grants SBR-0111140 (Aït-Sahalia), DMS-0204639 (Mykland and Zhang) and the NIH under grant RO1 AG023141-01 (Zhang) is also gratefully acknowledged.


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