时变条件异方差的贝叶斯模型

IF 4.9 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Bayesian Analysis Pub Date : 2020-09-13 DOI:10.1214/21-BA1267

Sayar Karmakar, Arkaprava Roy

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引用次数: 10

摘要

条件异方差（CH）模型通常用于分析金融数据集。具有时不变系数的经典模型（如ARCH-GARCH）通常不足以描述由于市场可变性而随时间的频繁变化。然而，通过考虑这些模型的时变类似物，我们可以获得更好的洞察力。在本文中，我们提出了一种贝叶斯方法来估计这些模型，并开发了基于哈密顿蒙特卡罗（HMC）采样的计算高效的MCMC算法。我们还根据平均Hellinger度量建立了随着样本量增加的后验收缩率。将我们的方法的性能与频率估计和时间常数类似物的估计进行了比较。最后，我们获得了一些流行的外汇（货币转换率）和股市数据集的时变参数估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bayesian Modelling of Time-Varying Conditional Heteroscedasticity

Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market variability. However we can achieve significantly better insight by considering the time-varying analogues of these models. In this paper, we propose a Bayesian approach to the estimation of such models and develop computationally efficient MCMC algorithm based on Hamiltonian Monte Carlo (HMC) sampling. We also established posterior contraction rates with increasing sample size in terms of the average Hellinger metric. The performance of our method is compared with frequentist estimates and estimates from the time constant analogues. To conclude the paper we obtain time-varying parameter estimates for some popular Forex (currency conversion rate) and stock market datasets.

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来源期刊

Bayesian Analysis 数学-数学跨学科应用

CiteScore

6.50

自引率

13.60%

发文量

审稿时长

>12 weeks

期刊介绍： Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.