Bayesian modeling of dynamic extreme values: Extension of generalized extreme value distributions with latent stochastic processes
Bayesian modeling of dynamic extreme values: Extension of generalized extreme value distributions with latent stochastic processes
复制标题
动态极值的贝叶斯建模：具有潜在随机过程的广义极值分布的扩展
DOI：
10.1080/02664763.2016.1201796
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发表时间：
2017
影响因子：
1.5
通讯作者：
Tsuyoshi Kunihama and Yasuhiro Omori
中科院分区：
文献类型：
--
作者：
Jouchi Nakajima;Tsuyoshi Kunihama and Yasuhiro Omori
本文发展了具有柔性时变潜在结构的极值模型的贝叶斯推理。利用广义极值分布将遵循自回归移动平均（ARMA）过程的状态变量与gumbel分布创新相结合。将随时间变化的极值分布与重尾误差项相结合。提出了一种有效的马尔可夫链蒙特卡罗算法，该算法使用有限混合正态分布的状态空间表示来近似Gumbel分布。通过模拟数据和两组不同的实际数据说明了该方法。将股票价格指数日收益率的月最小值和小时电力需求的月最大值拟合到模型中，并用于模型比较。估计结果表明了所提模型和方法的有效性，并证明了潜在自回归过程和重尾误差在描述最小库存收益和最大电力需求的月序列中起着重要作用。
This paper develops Bayesian inference of extreme value models with a flexible time-dependent latent structure. The generalized extreme value distribution is utilized to incorporate state variables that follow an autoregressive moving average (ARMA) process with Gumbel-distributed innovations. The time-dependent extreme value distribution is combined with heavy-tailed error terms. An efficient Markov chain Monte Carlo algorithm is proposed using a state-space representation with a finite mixture of normal distributions to approximate the Gumbel distribution. The methodology is illustrated by simulated data and two different sets of real data. Monthly minima of daily returns of stock price index, and monthly maxima of hourly electricity demand are fit to the proposed model and used for model comparison. Estimation results show the usefulness of the proposed model and methodology, and provide evidence that the latent autoregressive process and heavy-tailed errors play an important role to describe the monthly series of minimum stock returns and maximum electricity demand.