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The Annals of Statistics 2004, Vol. 32, No. 5, 21862222
 

Summary: The Annals of Statistics
2004, Vol. 32, No. 5, 21862222
DOI 10.1214/009053604000000427
Institute of Mathematical Statistics, 2004
ESTIMATORS OF DIFFUSIONS WITH RANDOMLY SPACED
DISCRETE OBSERVATIONS: A GENERAL THEORY
BY YACINE AT-SAHALIA1 AND PER A. MYKLAND2
Princeton University and University of Chicago
We provide a general method to analyze the asymptotic properties
of a variety of estimators of continuous time diffusion processes when
the data are not only discretely sampled in time but the time separating
successive observations may possibly be random. We introduce a new
operator, the generalized infinitesimal generator, to obtain Taylor expansions
of the asymptotic moments of the estimators. As a special case, our results
apply to the situation where the data are discretely sampled at a fixed
nonrandom time interval. We include as specific examples estimators based
on maximum-likelihood and discrete approximations such as the Euler
scheme.
1. Introduction. Most theoretical models in finance are spelled out in
continuous time [see, e.g., Merton (1992)], whereas the observed data are, by

  

Source: At-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University
Mykland, Per A. - Department of Statistics, University of Chicago

 

Collections: Mathematics