A NOTE ON THE NORMALIZED ERRORS IN ARCH AND STOCHASTIC VOLATILITY MODELS

It is well-known that conditional heteroskedasticity thickens the tail s of the unconditional distribution of an error term relative to its c onditional distribution, To what extent do imperfect forecasts of the conditional variance undo this tail thickening? This note considers th e effect of changing the quality of the information embodied in a fore cast of a conditional variance, Adding noise of a certain form thicken s the tails of the normalized errors, but decreasing the amount of inf ormation used in the forecast may or may not thicken the tails, We als o explore the relation between tail thickness and various notions of ' 'optimal'' volatility forecasts, The relationship is surprisingly comp licated.