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首页> 外文期刊>Journal of Time Series Analysis >A NON-GAUSSIAN FAMILY OF STATE-SPACE MODELS WITH EXACT MARGINAL LIKELIHOOD
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A NON-GAUSSIAN FAMILY OF STATE-SPACE MODELS WITH EXACT MARGINAL LIKELIHOOD

机译：具有精确边际似然的状态空间模型的非高斯族

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摘要

The Gaussian assumption generally employed in many state-space models is usually not satisfied for real time series. Thus, in this work, a broad family of non-Gaussian models is defined by integrating and expanding previous work in the literature. The expansion is obtained at two levels: at the observational level, it allows for many distributions not previously considered, and at the latent state level, it involves an expanded specification for the system evolution. The class retains analytical availability of the marginal likelihood function, uncommon outside Gaussianity. This expansion considerably increases the applicability of the models and solves many previously existing problems such as long-term prediction, missing values and irregular temporal spacing. Inference about the state components can be performed because of the introduction of a new and exact smoothing procedure, in addition to filtered distributions. Inference for the hyperparameters is presented from the classical and Bayesian perspectives. The results seem to indicate competitive results of the models when compared with other non-Gaussian state-space models available. The methodology is applied to Gaussian and non-Gaussian dynamic linear models with time-varying means and variances and provides a computationally simple solution to inference in these models. The methodology is illustrated in a number of examples.
机译：通常在许多状态空间模型中采用的高斯假设通常无法满足实时序列的要求。因此，在这项工作中，通过整合和扩展文献中的先前工作，定义了一系列非高斯模型。在两个级别获得扩展：在观察级别，它允许许多以前没有考虑的分布；在潜在状态级别，它涉及系统演化的扩展规范。该类保留了边际似然函数的分析可用性，这在高斯性之外并不常见。这种扩展极大地提高了模型的适用性，并解决了许多先前存在的问题，例如长期预测，缺失值和不规则的时间间隔。除了过滤分布之外，由于引入了新的精确平滑过程，因此可以执行关于状态分量的推断。从经典和贝叶斯角度介绍了超参数的推论。与其他可用的非高斯状态空间模型相比，该结果似乎表明该模型具有竞争性。该方法应用于具有时变均值和方差的高斯和非高斯动态线性模型，并为这些模型的推论提供了计算简单的解决方案。在许多示例中说明了该方法。

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