In this work, we propose a model for estimating volatility from financial time series, extending the non-Gaussian family of space-state models with exact marginal likelihood proposed by Gamerman, Santos and Franco (2013). On the literature there are models focused on estimating financial assets risk, however, most of them rely on MCMC methods based on Metropolis algorithms, since full conditional posterior distributions are not known. We present an alternative model capable of estimating the volatility, in an automatic way, since all full conditional posterior distributions are known, and it is possible to obtain an exact sample of parameters via Gibbs Sampler. The incorporation of jumps in returns allows the model to capture speculative movements of the data, so that their influence does not propagate to volatility. We evaluate the performance of the algorithm using synthetic and real data time series. Keywords: Financial time series, Stochastic volatility, Gibbs Sampler, Dynamic linear models.

中文翻译：

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通过 Gibbs 采样器跳跃的非高斯随机波动率模型

在这项工作中，我们提出了一个用于从金融时间序列估计波动率的模型，扩展了具有精确边际似然的非高斯空间状态模型系列，由 Gameman、Santos 和 Franco（2013）提出。在文献中，有一些模型专注于估计金融资产风险，但是，由于不知道完整的条件后验分布，因此大多数模型依赖于基于 Metropolis 算法的 MCMC 方法。我们提出了一种能够以自动方式估计波动率的替代模型，因为所有完整的条件后验分布都是已知的，并且可以通过 Gibbs Sampler 获得精确的参数样本。纳入回报跳跃允许模型捕捉数据的投机运动，因此它们的影响不会传播到波动性。我们使用合成和真实数据时间序列来评估算法的性能。关键词：金融时间序列，随机波动率，吉布斯采样器，动态线性模型。