Subsampling for APC stochastic processes

We investigate the problem of consistency of subsampling procedure for nonstationary almost periodically correlated (APC) processes. It is shown that an appropriately normalized estimator of covariance has a consistent subsampling version provided that some mild regularity conditions are fulfilled. The result allows to improve the tests related to APC models, and to get more exact confidence intervals for such models. At the end of the paper we discuss open questions related to the optimal choice of the subsampling window b and the speed of convergence of the procedure considered.