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Maximum Likelihood Estimates of a Class of One‐Dimensional Stochastic Differential Equation Models From Discrete Data
Author(s) -
Cleur Eugene M.
Publication year - 2001
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00238
Subject(s) - mathematics , discretization , stochastic differential equation , likelihood function , quadrature (astronomy) , function (biology) , stochastic process , differential equation , estimation theory , mathematical optimization , statistics , mathematical analysis , evolutionary biology , electrical engineering , biology , engineering
The problem of computing the maximum likelihood estimate of the parameters of a specific class of stochastic differential equation (SDE) models with linear drift whose sample paths are observed at discrete time points is considered. This estimate is obtained as in Cleur and Manfredi (1999) by discretizing the explicit expressions for the estimates which maximize the likelihood function in continuous time, by discretizing the likelihood function through a quadrature approximation before maximizing it, and by maximizing the likelihood function of the Euler scheme approximation to the underlying continuous process. Simulation results indicate that, for the constellation of parameter values considered, all three approaches lead to very similar results.