Estimating the predictability and the linearity of a process by kernels

On the basis of discrete-time process data for system identification (or time-series prediction), it would be very desirable to determine a priori how unpredictable and how nonlinear a process is. Showing how this can be done by adopting the framework of statistical estimation theory is the purpose of this paper. Inferring the predictability of a process is important for estimating in advance which prediction performance can be realistically expected from a model. The "degree" of nonlinearity of the underlying process should also be assessed before the design of a suitable model is undertaken. If the data do not reveal a markedly nonlinear character, the irrelevance of nonlinear models will be noticed in advance, thereby saving time which would otherwise be lost on an unnecessary search.