Abstract
We consider the problem of parametric inference from continuous sample paths of the diffusion processes {x(t)} generated by the system of possibly nonstationary and/or nonlinear Ito stochastic differential equations. We propose a new instrumental variable estimator of the parameter whose pivotal statistic has a Gaussian distribution for all possible values of parameter. The new estimator enables us to construct exact level-α confidence intervals and tests for the parameter in the possibly non-stationary and/or nonlinear diffusion processes. Applications to several non-stationary and/or nonlinear diffusion processes are considered as examples.
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This work was supported by Korea Research Foundation Grant (KRF-2001-015-DP0057).
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So, B.S. A new instrumental variable estimation for diffusion processes. Ann Inst Stat Math 57, 733–745 (2005). https://doi.org/10.1007/BF02915435
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DOI: https://doi.org/10.1007/BF02915435