Modification of two-step method in estimating the parameters of stochastic differential equation models

Two-step method is introduced as an alternative method to classical methods in estimating the drift and diffusion parameters of the Stochastic Differential Equations (SDEs) models. Previous studies indicated that this method provides high percentage of accuracy of the estimated diffusion parameter of Lotka-Volterra model with simulated data. In this paper, a new improvement of two-step method is acquired to avoid the chosen of knots by applying Nadaraya-Watson kernel regression estimator in the first step of this method as a replacement of regression spline with truncated power series basis. The estimated parameters of Bachelier model by using modified two-step method are presented, including comparisons between two different kernel bandwidth methods, namely Asymptotic Mean Integrated Square Error (AMISE) for optimal bandwidth and Maximum Likelihood Cross-Validation (MLCV) technique. The performance of the new proposed method is evaluated with different number of sample sizes by using simulated data. Results indicate high percentage of accuracy of the estimated drift and estimated diffusion parameters of Bachelier model when AMISE for optimal bandwidth is applied compared to MLCV technique.