We present in this paper a framework for performance prediction of parallel programs on hierarchical clusters. This framework is mainly designed for the use by the switching functions in parallel adaptive applications. Indeed, the principal referred objectives by this framework are the accuracy of the prediction and the rapidity of the prediction process. To achieve these objectives, our framework is based on two principal steps, the first is at the installation moment of the parallel application, and the second is at runtime. In the first step, we profile two components which are sequential kernels of the program and network performances. In order to model accurately these two components we have developed new strategies of regression. In the second step, we use the generated models and the runtime variables to the completion time estimation via our fast simulator MPI-PERF-SIM. Our experimentations on the Grid'5000 platform demonstrate the interest of this approach that can be the basis of adaptivity for parallel numerical libraries on dedicated hierarchical platforms.