2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136409This 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.Published at http://dx.doi.org/10.1214/009053606000001514 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62F05, 62M10 (Primary); 60G10 (Secondary)text