The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable...

This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of...

The paper by Atkinson, Riani and Ceroli, henceforth ARC, is concerned with detection of outliers and unsuspected structures which is rather important in practice.  This is done through a Forward Search Algorithm.  The statistical analysis of such algorithms poses many challenging problems, and...

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data.  This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000).  An asymptotic analysis of the Forward Search is...

An algorithm suggested by Hendry (1999) for estimation in a regression with more regressors than observations, is analyzed with the purpose of finding an estimator that is robust to outliers and structural breaks.  This estimator is an example of a one-step M-estimator based on Huber's skip...

Some examples of the regression method are compared with likelihood-based inference. It is shown that, although the asymptotic theory is distinctly different for ergodic and nonergodic processes, the likelihood methods lead to the result that asymptotic inference can be conducted in the same way...