Generalized extreme value distribution with time-dependence using the AR and MA models in state space form
Generalized extreme value distribution with time-dependence using the AR and MA models in state space form
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DOI：
10.1016/j.csda.2011.04.017
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发表时间：
2012-11-01
影响因子：
1.8
通讯作者：
Fruehwirth-Schnatter, Sylvia
中科院分区：
文献类型：
--
作者：
Nakajima, Jouchi;Kunihama, Tsuyoshi;Fruehwirth-Schnatter, Sylvia
提出了一种新的状态空间方法来模拟极值过程的时间依赖性。使用状态空间表示将广义极值分布扩展为包含时间相关性，其中状态变量遵循自回归(AR)过程或具有来自Gumbel分布的新息的移动平均(MA)过程。利用贝叶斯方法，提出了一种实现马尔可夫链蒙特卡罗方法的有效算法，其中我们利用了由十个正态分布组成的混合分布对冈贝尔分布的精确逼近。使用每日股票数据的极端回报来说明这一方法。该模型适用于最低收益率的月度序列，实证结果支持了观测到的最低收益率之间存在时间相关性的有力证据。(C)2011爱思唯尔B.V.保留所有权利。
A new state space approach is proposed to model the time-dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit an accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence of time-dependence among the observed minimum returns. (C) 2011 Elsevier B.V. All rights reserved.