Robust Time Series Regression

A research project of the Seminar für Statistik, ETH Zürich
Researchers: Christian Sangiorgio, Dr. Werner Stahel.

Abstract:

Multiple linear regression is one of the basic and best-known tools of applied statistics. If the random errors fail to be independent, the standard errors of the estimates obtained by the simple Least Squares methodology are wrong. A classical approach to the problem is based on developing a time series model for the residuals (estimated random errors) obtained from Least Squares, and then adjusting the calculation estimates and/or of standard errors on the basis of this model. The key words for these classical methods are Generalized Least Squares and Cochran-Orchutt procedure.

These classical methods are based on the assumption of a normal distribution for the random errors. Since this assumption is often unwarranted, robust methods have been developed in the last 30 years. Powerful general results are available for the class of M-estimators. They allow for a straightforward "robustification" of the mentioned classical methods. A number of extensions needs further resarch, which will be undertaken in this project.

Regression models with correlated errors -- as described -- are needed, among many other examples, when studying emissions of road traffic in so-called tunnel studies. Observed concentrations of air pollutants in a road tunnel in short time intervals are described as a function of the numbers of vehicles of different classes and of the traffic speed. Such a study has been conducted in 1993 in the Gubrist tunnel near Zürich and has been analyzed by our group using classical and robust methods. Further tunnel studies are planned by the Atmospheric Chemistry Group of the Labor für Atmosphärenphysik (LAPETH). Their analysis will be part of this project.


Back to the homepage of Werner Stahel or of the statistics group Seminar für Statistik of the Swiss Federal Institute of Technology (ETH) Zürich