There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the effect of nonstationarity on inference using these methods and compare them to model based inference using the cointegrated vector autoregressive model. Finally...

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...

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the...

Yule (1926) introduced the concept of spurious or nonsense correlation, and showed by simulation that for some nonstationary processes, that the empirical correlations seem not to converge in probability even if the processes were indpendent. This was later discussed by Granger and Newbold...

We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness...

The Forward Search Algorithm is a statistical algorithm for obtaining robust estimators of regression coefficients in the presence of outliers. The algorithm selects a succession of subsets of observations from which the parameters are estimated. The present note shows how the theory of...

Iterated one-step Huber-skip M-estimators are considered for regression problems. Each one-step estimator is a re-weighted least squares estimators with zero/one weights determined by the initial estimator and the data. The asymptotic theory is given for iteration of such estimators using a...

The Forward Search Algorithm is a statistical algorithm for obtaining robust estimators of regression coefficients in the presence of outliers. The algorithm selects a succession of subsets of observations from which the parameters are estimated. The present note shows how the theory of...

We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator...