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首页> 外文期刊>Journal of applied statistics >Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes
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Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes

机译：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

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摘要

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.
机译：本文利用具有时间依赖性的潜在结构来发展贝叶斯极值模型的推断。广义的极值分布用于结合遵循Gumbel分布的创新的自回归移动平均（ARMA）过程的状态变量。时间相关的极值分布与重尾误差项结合在一起。提出了一种有效的马尔可夫链蒙特卡罗算法，该算法使用状态空间表示与正态分布的有限混合来近似Gumbel分布。该方法通过模拟数据和两组不同的实际数据进行说明。股价指数的日收益的月最小值和小时用电量的月最大值与所提议的模型相适应，并用于模型比较。估计结果表明了所提模型和方法的有用性，并提供了证据，即潜在的自回归过程和重尾误差在描述每月最低库存收益和最大电力需求方面起着重要作用。

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