Data-driven estimation of semiparametric fractional autoregressive models

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. For selecting the bandwidth, the proposal of Beran and Feng (1999) based on the iterative plug-in idea (Gasser et al., 1991) is used. Asymptotic properties of the proposed algorithms are investigated. A large simulation study illustrates the practical performance of the methods.