Subsampling for continuous-time almost periodically correlated processes

In this work we investigate the problem of consistency of subsampling procedure for estimators in continuous time nonstationary stochastic processes with periodic or almost periodic covariance structure. The motivation for this work comes from the difficulty associated with handling the asymptotic distributions corresponding to estimates of second order characteristics for such nonstationary processes. It is shown that an appropriately normalized estimator has a consistent subsampling version provided that some mild regularity conditions are fulfilled. We also prove the mean square and almost everywhere consistency of our subsampling procedure. As a result of the research, we are able to construct the subsampling-based confidence intervals for the relevant characteristics of such nonstationary processes. We show that our results can be generalized to other nonstationary continuous time processes. At the end of the paper, simulations and real data applications are considered.