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摘要翻译：
本文研究了一类扰动具有有理概率密度函数的离散时间随机波动率模型的滤波问题。这包括具有奇数自由度的柯西分布和学生t-分布。利用状态空间的实现来表示有理概率密度函数，可以准确地解决滤波问题。然而，所涉及的状态空间矩阵的大小随着滤波器的每一个时间步长而呈指数增长。因此，我们采用随机平衡截断技术来逼近所涉及的高阶有理函数。仿真研究表明了该方法的适用性。此外，还导出了一种简单的矩量估计方法。
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英文标题：
《Filtering and estimation in stochastic volatility models with rationally
distributed disturbances》
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作者：
Bernard Hanzon and Wolfgang Scherrer
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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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：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：
This paper deals with the filtering problem for a class of discrete time stochastic volatility models in which the disturbances have rational probability density functions. This includes the Cauchy distributions and Student t-distributions with odd number of degrees of freedom. Using state space realizations to represent the rational probability density functions we are able to solve the filtering problem exactly. However the size of the involved state space matrices grows exponentially with each time step of the filter. Therefore we use stochastically balanced truncation techniques to approximate the high order rational functions involved. In a simulation study we show the applicability of this approach. In addition a simple method of moments estimator is derived.
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PDF链接：
https://arxiv.org/pdf/706.3335
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