A weighted least squares procedure to approximate least absolute deviation estimation in time series with specific reference to infinite variance unit root problems

Abstract

A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is large and for problems with many independent variables. In such problems bootstrap methods must often be utilized to test hypotheses and especially in such a case this procedure has an advantage over least absolute regression. The procedure will be illustrated on first-order autoregressive problems, including the random walk. A bootstrap procedure is used to test the unit root hypothesis and good results were found.