Discussiones
Mathematicae Probability and Statistics 21(1) (2001) 11-20

## TESTING ON THE FIRST-ORDER AUTOREGRESSIVE MODEL WITH CONTAMINATED
EXPONENTIAL WHITE NOISE FINITE SAMPLE CASE

Hocine Fellag

*Department of Mathematics *

Faculty of Sciences, University of Tizi-Ouzou

Tizi-Ouzou, 15000 Algeria

**e-mail:** hfellag@yahoo.com

## Abstract

The testing problem on the first-order autoregressive parameter in finite
sample case is considered. The innovations are distributed according to the exponential
distribution. The aim of this paper is to study how much the size of this test changes
when, at some time k, an innovation outlier contaminant occurs. We show that the test is
rather sensitive to these changes.

**Keywords:** autoregressive model, exponential distribution, outlier,
test.

**2000 Mathematics Subject Classification:** 62F11, 62M10.

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Received 10 April 2000

Revised 7 May 2001