Bernoulli

  • Bernoulli
  • Volume 1, Number 1-2 (1995), 17-39.

Martingale estimation functions for discretely observed diffusion processes

Bo Martin Bibby and Michael Sørensen

Full-text: Open access

Abstract

We consider three different martingale estimating functions based on discrete-time observations of a diffusion process. One is the discretized continuous-time score function adjusted by its compensator. The other two emerge naturally when optimality properties of the first are considered. Subject to natural regularity conditions, we show that all three martingale estimating functions result in consistent and asymptotically normally distributed estimators when the underlying diffusion is ergodic. Practical problems with implementing the estimation procedures are discussed through simulation studies of three specific examples. These studies also show that our estimators have good properties even for moderate sample sizes and that they are a considerable improvement compared with the estimator based on the unadjusted discretized continuous-time likelihood function, which can be seriously biased.

Article information

Source
Bernoulli, Volume 1, Number 1-2 (1995), 17-39.

Dates
First available in Project Euclid: 2 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1186078360

Mathematical Reviews number (MathSciNet)
MR1354454

Zentralblatt MATH identifier
0830.62075

Keywords
discrete-time sampling inference for diffusion processes optimality quasi-likelihood simulation stochastic differential equation

Citation

Martin Bibby, Bo; Sørensen, Michael. Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1 (1995), no. 1-2, 17--39. https://projecteuclid.org/euclid.bj/1186078360


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