Abstract:

We approximate interest rate financial data by homogeneous diffusion process with piecewise constant coefficients. Both drift and diffusion terms are estimated nonparametrically. For estimating of the drift term we use the taut string method which minimizes the numbers of peaks but for the diffusion term we minimize the number of intervals of constancy. For both estimators consistency is proved and convergence rate is calculated. Also the efficacy of the methods is demonstrated using simulated data.