## How often to sample a continuous-time process in the presence of market microstructure noise (2005)

Venue: | Review of Financial Studies |

Citations: | 86 - 13 self |

### BibTeX

@ARTICLE{Aït-sahalia05howoften,

author = {Yacine Aït-sahalia and Per A. Mykland and Lan Zhang},

title = {How often to sample a continuous-time process in the presence of market microstructure noise},

journal = {Review of Financial Studies},

year = {2005},

volume = {18},

pages = {351--416}

}

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### OpenURL

### 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 derives its closed-form expression. But even with optimal sampling, using say 5-min returns when transactions are recorded every second, a vast amount of data is discarded, in contradiction to basic statistical principles. We demonstrate that modeling 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. Over the past few years, price data sampled at very high frequency have become increasingly available in the form of the Olsen dataset of currency exchange rates or the TAQ database of NYSE stocks. If such data were not affected by market microstructure noise, the realized volatility of the process (i.e., the average sum of squares of log-returns sampled at high frequency) would estimate the returns ’ variance, as is well known. In fact, sampling as often as possible would theoretically produce in the limit a perfect estimate of that variance. We start by asking whether it remains optimal to sample the price process at very high frequency in the presence of market microstructure noise, consistently with the basic statistical principle that, ceteris paribus, more data are preferred to less. We first show that, if noise is present but unaccounted for, then the optimal sampling frequency is finite, and we We are grateful for comments and suggestions from the editor, Maureen O’Hara, and two anonymous