Estimation of confidence regions for the parameters of ARMA models guaranteed non-asymptotic results

In this paper we consider the problem of estimating confidence regions for the parameters of ARMA 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 region containing the true parameters with guaranteed probability is then obtained. All results hold true for a finite number of data points and no asymptotic theory is used. The usefulness of the approach is illustrated in a simulation example.