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.
"Testing for change points in time series models and limiting theorems for NED sequences." Ann. Statist. 35 (3) 1213 - 1237, July 2007. https://doi.org/10.1214/009053606000001514