A Note on the Normalized Errors in ARCH and Stochastic Volatility Models
研究了条件方差预测质量变化如何影响标准化误差的尾部厚度，发现添加特定噪声会增厚尾部，但减少预测信息的影响不确定，且尾部厚度与“最优”波动率预测的关系复杂。
It is well-known that conditional heteroskedasticity thickens the tails of the unconditional distribution of an error term relative to its conditional distribution. To what extent do imperfect forecasts of the conditional variance undo this tail thickening? This note considers the effect of changing the quality of the information embodied in a forecast of a conditional variance. Adding noise of a certain form thickens the tails of the normalized errors, but decreasing the amount of information used in the forecast may or may not thicken the tails. We also explore the relation between tail thickness and various notions of “optimal” volatility forecasts. The relationship is surprisingly complicated.