Ling, Shiqing, Testing for Change Points in Time Series Models and Limiting Theorems for NED Sequences, Annals of statistics , 35(3), 2007, pp. 1213-1237
This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.