A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic diﬀerential equations. We specify a parametric class of diﬀusions and estimate the parameters of interest by minimizing criteria based on the integrated squared diﬀerence between kernel estimates of the drift and diﬀusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete-time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on inﬁll and long span asymptotics and is robust to deviations from stationarity, requiring only recurrence.
Bandi, Federico M. and Phillips, Peter C.B., "A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions" (2005). Cowles Foundation Discussion Papers. 1806.