HOW OFTEN TO SAMPLE A CONTINUOUS-TIME PROCESS IN THE PRESENCE OF MARKET MICROSTRUCTURE NOISE

Yacine Ait-Sahalia
(joint work with Per Mykland and Lan Zhang)

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 derive its closed-form expression. But even with optimal sampling, using say five minute returns when transactions are recorded every second, a vast amount of data is discarded, in contradiction to basic statistical principles. We demonstrate that modelling 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.