Subsampling for Nonstationary Time Series

Abstract

Stationary time series are very convenient to work with from a mathematical point of view, but the assumption of stationarity is often violated when modeling real-life data. To mention only two examples, many economic time series exhibit seasonal fluctuations, while stock return data typically show time-dependent variability. The goal of this chapter is to demonstrate that the subsampling method is by no means restricted to stationary series. We will provide sufficient conditions under which asymptotically correct inference can be made even in the presence of nonstationarity. In outline and style, this chapter follows the previous one very closely. In particular, the subsampling methodology for nonstationary observations will be identical to the one for stationary observations. Many of the results derived under stationarity will be restated and reproven under weaker conditions. Much of what is presented is taken from Politis, Romano, and Wolf (1997).