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 highfrequency estimates their variance. When market microstructurenoise is present but unaccounted for, however, we show thatthe optimal sampling frequency is finite and derives its closed-formexpression. But even with optimal sampling, using say 5-minreturns when transactions are recorded every second, a vastamount of data is discarded, in contradiction to basic statisticalprinciples. We demonstrate that modeling the noise and usingall the data is a better solution, even if one misspecifiesthe noise distribution. So the answer is: sample as often aspossible.