Journal of Economic Theory and Econometrics: Journal of the Korean Econometric Society

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Journal of Economic Theory and Econometrics
Journal of the Korean Econometric Society

A Survey Study on the Estimation Techniques for Diffusion Processes

Vol.16, No.2, June , 63–121

English Version |  Korean Version
  •   (Korea Securities Research Institute)


This study comprehensively investigates the state-of-the-art estimation theory of diffusion processes. In the econometrics literature, there are now a number of important works on diffusion process estimation. In particular, statistical methods for minimizing the discretization bias in diffusion estimation continues to be an active area of research, which is another main issues addressed in this study. A comprehensive discussion of diffusion process estimation theory is presented as well as a review and comparison the most recent estimation techniques. The rapid progress of the modern computer has accelerated simulation-based estimation techniques, which is discussed thoroughly in this study. The simulation maximum likelihood estimation (SMLE), including its variant that uses importance sampling, as well as the Bayesian Markov chain Monte-Carlo (MCMC) technique have become important tools in simulation-based estimation. Many existing literatures tend to confuse the function of importance samplers in SMLE that use importance sampling with the proposal distribution of the Bayesian MCMC, both of which are mistakenly thought to be similar concepts. In this paper, the difference between the two is explicitly explained. In addition, a systematic classification of diffusion process estimation techniques is proposed. From which, the relationship and difference between the established diffusion process estimations are categorized, and suggestions on future research on diffusion process estimation is inferred.

   Diffusion Process, Discretization Bias, Simulation Maximum Likelihood Estimation (SMLE), SMLE with Importance Sampler, Bayesian Markov Chain Monte-Carlo (MCMC), Importance Sampler Function, Proposal Distribution, Metropolis-Hastings Algorithm, Gibbs-Sampl

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