Data driven confidence intervals for diffusion process using double smoothing empirical likelihood

In this paper, we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it. Compared with double smoothing local constant estimator, double smoothing local linear estimator proposed in this paper is an inventive estimation method. Moreover, we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation, since the latter undermines the predictability of the estimator. Accordingly, new algorithm for simulation is proposed. Through Monte Carlo simulation and empirical analysis, both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate, etc.