Decades of daily data versus one week data with ultra-high frequency: a note on estimating expected rate of return and volatility

Are twodecades of daily observations more plausible thana set of hourly data of the same size? Is it true that the more data there is the better the estimate? To answer those questions, an understanding of two types of consistency associated with estimates of return andvolatility is fundamental. The first consistency depends critically upon the total length of observation period and reciprocates with estimation of return; while the second emphasizes the role of sampling frequency and is more relevant when dealing with estimation of volatility. This letter addresses certain important issues from estimating return and volatility with focuses on the nature and the distinction of these two consistencies as well as their respective empirical implications.