Globally optimal parameter estimates for nonlinear diffusions
Mijatović, Aleksandar and Schneider, Paul. (2010) Globally optimal parameter estimates for nonlinear diffusions. Annals of statistics, Vol.38 (No.1). pp. 215-245. ISSN 0090-5364Full text not available from this repository.
Official URL: http://dx.doi.org/10.1214/09-AOS710
This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of nonlinear SDEs with constant volatility and drift that is linear in the model parameters. In this setting, globally optimal parameters are obtained in a single step by solving a linear system. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.
|Item Type:||Journal Article|
|Subjects:||H Social Sciences > HG Finance|
|Divisions:||Faculty of Social Sciences > Warwick Business School > Finance Group
Faculty of Social Sciences > Warwick Business School
|Journal or Publication Title:||Annals of statistics|
|Publisher:||Inst Mathematical Statistics|
|Number of Pages:||31|
|Page Range:||pp. 215-245|
|Access rights to Published version:||Restricted or Subscription Access|
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