REGRESSION AND AUTOREGRESSION WITH INFINITE VARIANCE.

The theory of the linear model is incomplete in that it fails to deal with variables possessing infinite variance. To fill an important part of this gap, an unbiased estimate, the ″screened ratio estimate″ , is given for lambda in the regression E(X vertical Z) equals lambda Z; X and Z are linear combinations of independent, identically distributed symmetric random variables that are either stable or asymptotically Pareto distributed of index alpha less than equivalent to 2. The consistency of least squares estimates for finite moving averages is established.