Non-asymptotic confidence sets for the parameters of ARMAX models

Abstract

In this paper we consider the problem of constructing confidence sets for the parameters of ARMAX models. Based on subsampling techniques and building on earlier exact finite sample results due to Hartigan, we compute the exact probability that the true parameters belong to certain regions in the parameter space. By intersecting these regions, a confidence set containing the true parameters with guaranteed probability is obtained. All results hold rigorously true for any finite number of data points and no asymptotic theory is involved. Moreover, prior knowledge on the uncertainty affecting the data is reduced to a minimum. A simulation example is provided showing that the method delivers practically useful confidence sets with guaranteed probabilities.