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 Zieliki (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.