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.

References

[1] C.B. Bell and E.P. Smith, Inference for non-negative autoregressive schemes, Communication in Statistics, Theory and Methods, 15 (8) (1986), 2267-2293.
[2] Y. Berkoun, H. Fellag, M. Ibazizen and R. Zieliński, Maximal size of the student and the Anova tests under exactly one contaminant, Journal of Mathematical Sciences 81, (5) (1996), 2900-2904.
[3] A.J. Fox, Outliers in time series, J. Roy. Stat. Soc. 34 (B) (1972), 350-363.
[4] D.P. Gaver and P.A.W. Lewis, First-order autoregressive Gamma sequences and point process, Adv. Appl. Prob. 12 (1980), 727-745.
[5] G. Saporta, Probabilités, Analyses des données et Statistique, Technip Ed. (1990).
[6] M.A.A. Turkman, Bayesian analysis of an autoregressive process with exponential white noise, Statistics 21 (4) (1990), 601-608.

Received 10 April 2000
Revised 7 May 2001