Parameter identification in mixed Brownian–fractional Brownian motions using Powell's optimization algorithm

This paper deals with the problem of estimating the parameters of mixed Brownian–fractional Brownian motions with the combination of maximum likelihood approach and Powell's method. The maximum likelihood estimators are obtained based on the approximation by random walks of the driving noise. By adapting the Powell fast optimization algorithm, these estimators can be efficiently computed by computer software. The performance of our method is tested on simulated mixed Brownian–fractional Brownian motion data sets, and is compared with the approach proposed by Filatova (2008).