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.     

Testing continuous-time models of the spot interest rate

Different continuous-time models for interest rates coexistin the literature. We test parametric models by comparing theirimplied parametric density to the same density estimated nonparametrically.We do not replace the continuous-time model by discrete approximations,even though the data are recorded at discrete intervals. Theprincipal source of rejection of existing models is the strongnon-linearity of the drift. Around its mean, where the driftis essentially zero, the spot rate behaves like a random walk.The drift then mean-reverts strongly when far away from themean. The volatility is higher when away from the mean.