Semiparametric GARCH via Bayesian Model Averaging

As the dynamic structure of financial markets is subject to dramatic change, a model capable of providing consistently accurate volatility estimates should not make rigid assumptions on how prices change over time. Most volatility models impose a particular parametric functional form that relates an observed price change to a volatility forecast (news impact function). Here, a new class of functional coefficient semiparametric volatility models is proposed, where the news impact function is allowed to be any smooth function. The ability of the proposed model to estimate volatility is studied and compared to the well-known parametric proposals, in both a simulation study and an empirical study with real financial market data. The news impact function is estimated using a Bayesian model averaging approach, implemented via a carefully developed Markov chain Monte Carlo sampling algorithm. Using simulations it is shown that the proposed flexible semiparametric model is able to learn the shape of the news impact function very effectively, from observed data. When applied to real financial time series, the proposed model suggests that news impact functions have quite different shapes over different asset types, but a consistent shape within the same asset class. Supplementary materials for this article are available online.

鉴于金融市场的动态结构会发生剧烈变动，能够持续提供精准波动率估计的模型，不应就价格随时间的演化路径施加刚性假设。多数波动率模型会设定特定的参数化函数形式，将观测到的价格变动与波动率预测建立关联，该类函数即新闻冲击函数（news impact function）。本文提出一类全新的函数系数半参数波动率模型，该模型允许新闻冲击函数为任意光滑函数。本文通过模拟实验与真实金融市场数据的实证研究，对所提模型的波动率估计能力展开研究，并与主流的参数化波动率模型进行对比。本文采用贝叶斯模型平均（Bayesian model averaging）方法估计新闻冲击函数，并通过精心设计的马尔可夫链蒙特卡洛（Markov chain Monte Carlo）采样算法实现该方法。模拟实验结果表明，所提出的灵活半参数模型能够从观测数据中高效地学习新闻冲击函数的形态。将该模型应用于真实金融时间序列后发现，不同资产类型的新闻冲击函数形态差异显著，但同一资产类别内的新闻冲击函数形态保持一致。本文的补充材料可在线获取。