Generalized subsampling procedure for non-stationary time series

Abstract

In this paper, we propose a generalization of the subsampling procedure for non-stationary time series. The proposed generalization is simply related to the usual subsampling procedure. We formulate the sufficient conditions for the consistency of such a generalization. These sufficient conditions are a generalization of those presented for the usual subsampling procedure for non-stationary time series. Finally, we demonstrate the consistency of the generalized subsampling procedure for the Fourier coefficient in mean expansion of Almost Periodically Correlated time series.