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 paper studies cointegration in non-linear error correction models characterized by discontinuous and regime-dependent error correction and variance specifications. In addition the models allow for autoregressive conditional heteroscedasticity (ARCH) type specifications of the variance. The...

We address the IGARCH puzzle by which we understand the fact that a GARCH(1,1) model fitted by quasi maximum likelihood estimation to virtually any financial dataset exhibit the property that alpha^hat + beta^hat is close to one. We prove that if data is generated by certain types of continuous...

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 purpose of the present paper is to analyse a simple bubble model suggested by Blanchard and Watson. The model is defined by y(t) =s(t)¿y(t-1)+e(t), t=1,…,n, where s(t) is an i.i.d. binary variable with p=P(s(t)=1), independent of e(t) i.i.d. with mean zero and finite variance. We take ¿1...

The purpose of the present paper is to analyse a simple bubble model suggested by Blanchard and Watson. The model is defined by y(t) =s(t)?y(t-1)+e(t), t=1,…,n, where s(t) is an i.i.d. binary variable with p=P(s(t)=1), independent of e(t) i.i.d. with mean zero and finite variance. We take ?1...

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...