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协整VAR模型的自适应贝叶斯MCMC与秩选择

文章 arXiv papers · 作者: Gareth W. Peters et al.
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总结

本文提出一种用于贝叶斯协整向量自回归模型的自适应矩阵变量马尔可夫链蒙特卡洛方法。该方法以自动化的自适应 Metropolis 方法取代分组 Gibbs 抽样，旨在使具有相关参数块的高维系统也能进行实际可行的后验估计。模型的协整秩也被视为未知，从而可通过贝叶斯后验和贝叶斯因子分析联合推断秩与模型参数。

作者通过一个十变量模型展示该方法，其后验参数维度达到 310，并将该方法定位为交易系统的计算基础，可用于货币篮子等多资产工具。作者认为，随机秩推断能够以一致的统计框架适应不断变化的市场状况。所提供的文本介绍了方法贡献和一个示例，但没有提供交易表现、实施成本，也没有证据表明秩自适应能改善实盘策略结果。

核心观点

  • 研究提出使用自适应 Metropolis 抽样，替代贝叶斯协整 VAR 的分组 Gibbs 抽样。
  • 该抽样器面向具有相关矩阵参数块的高维模型。
  • 模型将协整秩视为不确定，并与模型参数联合推断。
  • 研究使用贝叶斯因子比较候选秩。
  • 一个十变量示例展示了计算规模，但未提供交易表现证据。

标签

统计学机器学习配对交易投资组合构建
全文
# Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model


# Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model









This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorithm of Roberts and Rosenthal, (2009). Developing the adaptive MCMC framework for Bayesian CVAR models allows for efficient estimation of posterior parameters in significantly higher dimensional CVAR series than previously possible with existing griddy Gibbs samplers. For a n-dimensional CVAR series, the matrix-variate posterior is in dimension $3n^2 + n$, with significant correlation present between the blocks of matrix random variables. We also treat the rank of the CVAR model as a random variable and perform joint inference on the rank and model parameters. This is achieved with a Bayesian posterior distribution defined over both the rank and the CVAR model parameters, and inference is made via Bayes Factor analysis of rank. Practically the adaptive sampler also aids in the development of automated Bayesian cointegration models for algorithmic trading systems considering instruments made up of several assets, such as currency baskets. Previously the literature on financial applications of CVAR trading models typically only considers pairs trading (n=2) due to the computational cost of the griddy Gibbs. We are able to extend under our adaptive framework to $n >> 2$ and demonstrate an example with n = 10, resulting in a posterior distribution with parameters up to dimension 310. By also considering the rank as a random quantity we can ensure our resulting trading models are able to adjust to potentially time varying market conditions in a coherent statistical framework.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。