摘要翻译：
本文提出了一种求解贝叶斯协整向量自回归(CVAR)的矩阵变量自适应马尔可夫链蒙特卡罗(MCMC)方法。我们用一种基于Roberts和Rosenthal(2009)的自适应Metropolis算法的自动高效替代方法取代了包括griddy Gibbs在内的贝叶斯CVAR模型抽样的流行方法。开发贝叶斯CVAR模型的自适应MCMC框架允许在比现有griddy Gibbs采样器更高维的CVAR序列中有效地估计后验参数。对于n维CVAR序列，矩阵变量的后验值为3n^2+n$,矩阵随机变量块之间存在显著的相关关系。我们还将CVAR模型的秩看作一个随机变量，并对秩和模型参数进行联合推理。这是通过定义在秩和CVAR模型参数上的贝叶斯后验分布来实现的，并通过秩的贝叶斯因子分析进行推断。实际上，自适应采样器还有助于为算法交易系统开发自动化的贝叶斯协整模型，考虑由几种资产组成的工具，如货币篮子。以前，由于griddy Gibbs的计算成本，CVAR交易模型的金融应用文献通常只考虑成对交易(n=2)。我们能够在我们的自适应框架下扩展到$n>>2$，并演示了一个n=10的示例，结果是参数达到310维的后验分布。通过将秩看作一个随机量，我们可以确保我们的交易模型能够在一个一致的统计框架中适应潜在的时变市场条件。
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英文标题：
《Model Selection and Adaptive Markov chain Monte Carlo for Bayesian
  Cointegrated VAR model》
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作者：
Gareth W. Peters and Balakrishnan Kannan and Ben Lasscock and Chris
  Mellen
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/1004.3830