How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise
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.
Authors: Yacine Aı̈t-Sahalia, Per A. Mykland, Lan Zhang
Citations: 928
Published: 2005-01-01T00:00:00.000Z
Why It Matters
Venue: Review of Financial Studies. Year: 2005. Citations: 928. Abstract signal: 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 fi...
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.
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