英文文献：Modelling Changes in the Unconditional Variance of Long Stock Return Series-建立长期股票收益序列无条件方差的变化模型
英文文献作者：Cristina Amado,Timo Ter?svirta
英文文献摘要：
In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long return series. For the purpose, we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Ter?svirta (2011). The latter component is modelled by incorporating smooth changes so that the unconditional variance is allowed to evolve slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the long-memory property in volatility may be explained by ignored changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecast accuracy of the new model over the GJR-GARCH model at all horizons for a subset of the long return series.

在这篇论文中，我们开发了一个测试和建模程序来描述长期波动波动在非常长的回报序列。为了达到这个目的，我们假设波动率被成倍地分解为一个有条件的和一个无条件的组件，就像Amado和Terasvirta(2011)中那样。后一个组件是通过合并平滑的变化来建模的，这样无条件的变化就可以随着时间慢慢地发展。统计推断用于指定时变分量的参数化，采用一系列拉格朗日乘子检验。模型的建立过程是用一个应用来说明道琼斯工业平均股票指数涵盖90多年的日收益。主要结论如下。首先，LM检验强烈拒绝无条件方差不变的假设。其次，研究结果表明，波动率的长记忆特性可以用忽略长序列无条件方差的变化来解释。最后，基于正式的统计检验，我们发现新模型的波动率预测精度优于GJR-GARCH模型在所有层面的长期收益序列的子集。