Test Of Diffusion Process Based On Bootstrap

In financial research field, there is relatively little effort on the specification test of diffusion process. Models misspecification often lead to incorrect statistical inference, which may result in errors of deviations hedging, asset pricing and risk management. Therefore, finding a good testing method for the diffusion process is necessary.In this paper, we make improvements on the basis of Corradi (2005) and Bhardwaj (2008) diffusion model specification test theory. Firstly, for the defects that block Bootstrap method only suit to stationary distribution process and determining method of test statistics quantile is unreasonable, we propose conditional Bootstrap method and discuss the asymptotic distribution based on conditional Bootstrap test statistics. Then, conditional Bootstrap method of model specification test is extended to the comparison of two diffusion models. By comparing two samples’ empirical conditional distribution function, we establish the test statistics and obtain asymptotical distribution of test statistics. Through the simulation analysis of geometric Brownian motion and CIR model, inspected the levels and effectiveness of conditional Bootstrap test method.