Estimation of Continuous-Time Markov Processes Sampled at Random Time Intervals Forthcoming: Econometrica

We introduce a family of generalized-method-of-moments estimators of the parameters of a continuous-time Markov process observed at random time intervals. The results include strong consistency, asymptotic normality, and a characterization of standard errors. Sampling is at an arrival intensity that is allowed to depend on the underlying Markov process and on the parameter vector to be estimated. We focus on financial applications, including tick-based sampling, allowing for jump diffusions, regime-switching diffusions, and reflected ∗Duffie is at the Graduate School of Business, Stanford University, Stanford CA 943055015 (email: [email protected]). Glynn is at the Management Science and Engineering Department, Stanford University, Stanford CA 94305 (email: [email protected]). We are especially grateful to Qiang Dai for extensive research assistance and discussions, to Jun Liu and Mark Garmaise for additional research assistance, to Tom Kurtz for helpful suggestions, and to Yacine Aı̈t-Sahalia for early formative discussions that contributed to the choice of this approach. We are also grateful for comments from several anonymous referees, Lars Hansen, Joel Hasbrouck, Mathias Kessler, Alain Monfort, and Michael Sørensen; and from participants of conferences or seminars at INRIA, Sophia-Antipolis, France; Department of Management, Odense University, Denmark; The Department of Mathematics, Humboldt University, Berlin; the Department of Mathematics, Stanford University; The Department of Statistics, Columbia University; The Institute of Advanced Studies, Princeton University; The Mathematical Sciences Research Institute, Berkeley; The Graduate School of Business, University of Chicago; and CREST-INSEE, Paris. We acknowledge hospitality offered to the first author by Mishkenot Sha’ananim, Jerusalem. 2 diffusions.