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

Summary: How Often to Sample a Continuous-Time
Process in the Presence of Market
Microstructure Noise
Yacine AiĘt-Sahalia
Princeton University and NBER
Per A. Mykland
The University of Chicago
Lan Zhang
Carnegie Mellon University
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 transac-
tions 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


Source: A´t-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University
Mykland, Per A. - Department of Statistics, University of Chicago


Collections: Mathematics