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

TLDR

High‑frequency log‑return variance is estimated by summing squared returns, yet even with optimal sampling, discarding data by aggregating to 5‑minute intervals contradicts basic statistical principles. The authors derive a closed‑form expression for the finite optimal sampling frequency when market microstructure noise is present but unaccounted for. Modeling the noise and using all data, even with misspecified noise distribution, yields better results, implying that sampling as often as possible is optimal.

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.