MEASURING STATIONARITY IN LONG-MEMORY PROCESSES

作者：Sen Kemal^*; Preuss Philip^*; Dette Holger^*

来源：Statistica Sinica, 2016, 26(1): 313-357.

DOI：10.5705/ss.2014.039

• Bootstrap
• empirical spectral measure
• goodness-of-fit tests
• integrated periodogram
• locally stationary process
• long-memory
• non-stationary processes
• spectral density

In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an L-2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a by-product of independent interest it is demonstrated that the two approaches behave differently in the limit.

• 出版日期2016-1