Approximating fragmented functional data by segments of Markov chains

We consider curve extension and linear prediction for functional data observed only on a part of their domain, in the form of fragments. We suggest an approach based on a combination of Markov chains and nonparametric smoothing techniques, which enables us to extend the observed fragments and construct approximated prediction intervals around them, construct mean and covariance function estimators, and derive a linear predictor. The procedure is illustrated on real and simulated data.