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

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