Estimating Continuous-Time Models with Discretely Sampled Data∗

This lecture surveys the recent literature on estimating continuous-time models using discrete observations. I start with the simplest possible framework and review different possible approaches as I progressively relax the assumptions made, to include different data generating processes (such as multivariate diffusions or jump processes), different observation schemes (such as incorporating market microstructure noise) and different sampling schemes (such as allowing for random time intervals.) ∗Invited Lecture, 2005 World Congress of the Econometric Society. I am grateful to Oliver Linton, the discussant, for many useful comments. Financial support from the NSF under grant SBR-0350772 is also gratefully acknowledged.