摘要翻译:
利用Markov链Monte Carlo(MCMC)技术研究了相关扩散过程的似然推理问题。这样的任务提出了两个有趣的问题。首先,MCMC格式的构造应保证相关系数的更新服从扩散矩阵的正定约束。第二,扩散只能在有限的点集上观测到,基于这些观测的参数的边际似然性通常是不可用的。我们利用扩散矩阵上的Cholesky分解克服了第一个问题。为了解决似然不可用问题,我们将Roberts和Stramer(2001Biometrika88(3):603-621)的数据增强框架推广到包括多元随机波动率模型在内的D维相关扩散模型。我们的方法通过基于模拟的实验和每日欧元/美元、英镑/美元汇率及其隐含的挥发进行了说明。
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英文标题:
《Likelihood-based inference for correlated diffusions》
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作者:
Konstantinos Kalogeropoulos, Petros Dellaportas, Gareth O. Roberts
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最新提交年份:
2007
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分类信息:
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:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorisation on the diffusion matrix. To deal with the likelihood unavailability, we generalise the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities.
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PDF链接:
https://arxiv.org/pdf/0711.1595