Volatility clustering is a common phenomenon in financial time series. Typically, linear models are used to describe the temporal autocorrelation of the (logarithmic) variance of returns. Considering the difficulty in estimation of this model, we construct a Dynamic Bayesian Network, which utilizes the conjugate prior relation of normal-gamma and gamma-gamma, so that at each node, its posterior form locally remains unchanged. This makes it possible to quickly find approximate solutions using variational methods. Furthermore, we ensure that the volatility expressed by the model is an independent incremental process after inserting dummy gamma nodes between adjacent time steps. We have found that, this model has two advantages: 1) It can be proved that it can express heavier tails than Gaussians, i.e., have positive excess kurtosis, compared to popular linear models. 2) If the variational inference(VI) is used for state estimation, it runs much faster than Monte Carlo(MC) methods, since the calculation of the posterior uses only basic arithmetic operations. And, its convergence process is deterministic. We tested the model, named Gam-Chain, using recent Crypto, Nasdaq, and Forex records of varying resolutions. The results show that: 1) In the same case of using MC, this model can achieve comparable state estimation results with the regular lognormal chain. 2) In the case of only using VI, this model can obtain accuracy that are slightly worse than MC, but still acceptable in practice; 3) Only using VI, the running time of Gam-Chain, under the most conservative settings, can be reduced to below 20% of that based on the lognormal chain via MC.

该论文提出了一种名为Gam-Chain的动态贝叶斯网络模型，可用于预测金融时间序列中的波动，并通过插入Dummy Gamma节点来保证模型中的波动是独立增量过程，相比于传统线性模型具有更好的拟合效果和更快的状态估计速度，并在加密货币、纳斯达克和外汇数据的实验中验证了其有效性。

用连锁伽马分布对随机游走波动进行建模