Stability of first-order autoregressive models Case of small samples

This book studies the stability of estimators of autoregressive models in the case of finite samples (nonasymptotic setup). The stability is one of aspects of approaches of robustness proposed by Zieliñki (institute of mathematics, academy of sciences, Warsaw, Poland). When an autoregressive model is violated, the well known least square estimator presents a high variability which makes this estimator rather useless. An unexpected fact we discovered is the lack of monotonicity of the bias when the amount of contamination is growing. Similar effects for the Student and ANOVA tests are studied in this document. Also, a review on various approaches of robustness and some results on estimation of a gaussian autoregressive model are presented. This document is very useful for beginners in research works connected with robust inference in time series.

Autorentext
Professor at Mouloud Mammeri University of Tizi-Ouzou, Algeria. Author of refered papers on robustness in time series, Bayesian and decision analysis. Supervisor of many PhD theses. Vice president in charge of international relations from 2005 until 2010. Coordinator of two international projects on decisión analysis and communication.