## The Annals of Statistics

### Testing for change points in time series models and limiting theorems for NED sequences

Shiqing Ling

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 35, Number 3 (2007), 1213-1237.

Dates
First available in Project Euclid: 24 July 2007

https://projecteuclid.org/euclid.aos/1185304004

Digital Object Identifier
doi:10.1214/009053606000001514

Mathematical Reviews number (MathSciNet)
MR2341704

Zentralblatt MATH identifier
1194.62017

#### Citation

Ling, Shiqing. Testing for change points in time series models and limiting theorems for NED sequences. Ann. Statist. 35 (2007), no. 3, 1213--1237. doi:10.1214/009053606000001514. https://projecteuclid.org/euclid.aos/1185304004

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