英文标题：
《Sparse Kalman Filtering Approaches to Covariance Estimation from High
Frequency Data in the Presence of Jumps》
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作者：
Michael Ho, Jack Xin
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最新提交年份：
2016
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英文摘要：
Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-EM (KEM) algorithm. However the KEM approach assumes log-normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix. In this paper we extend the KEM algorithm to price models that include jumps. We propose two sparse Kalman filtering approaches to this problem. In the first approach we develop a Kalman Expectation Conditional Maximization (KECM) algorithm to determine the un- known covariance as well as detecting the jumps. For this algorithm we consider Laplace and the spike and slab jump models, both of which promote sparse estimates of the jumps. In the second method we take a Bayesian approach and use Gibbs sampling to sample from the posterior distribution of the covariance matrix under the spike and slab jump model. Numerical results using simulated data show that each of these approaches provide for improved covariance estima- tion relative to the KEM method in a variety of settings where jumps occur.
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中文摘要：
从高频数据估计资产收益的协方差矩阵由于异步收益、市场微观结构噪声和跳跃而变得复杂。解决异步回报和市场微观结构的一种技术是卡尔曼EM（KEM）算法。然而，KEM方法假设对数正态价格，不解决回报过程中的跳跃，这可能会破坏协方差矩阵的估计。在本文中，我们将KEM算法扩展到包含跳跃的价格模型。我们提出了两种稀疏卡尔曼滤波方法来解决这个问题。在第一种方法中，我们开发了一种卡尔曼期望条件最大化（KECM）算法来确定未知协方差并检测跳跃。对于该算法，我们考虑了拉普拉斯模型和尖峰跳和板跳模型，这两种模型都促进了对跳的稀疏估计。在第二种方法中，我们采用贝叶斯方法，并使用Gibbs采样从尖峰和板跳模型下协方差矩阵的后验分布中采样。使用模拟数据的数值结果表明，在发生跳跃的各种情况下，与KEM方法相比，每种方法都提供了改进的协方差估计。
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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：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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