Non-Gaussian State—Space Modeling of Nonstationary Time Series
非平稳时间序列的非高斯状态空间建模AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究非平稳时间序列，并将均值的突变与渐变作为非高斯状态空间建模的重要对象。
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非平稳时间序列的非高斯状态空间建模
- 研究问题
- 如何在状态空间框架中处理均值的突变与渐变、重尾观测和离散数据，并实现非高斯非平稳序列的状态估计？
- 方法与思路
- 作者允许系统噪声和观测噪声非高斯，给出预测、滤波和平滑递推，并以密度函数的分段线性近似实现数值计算。
- 材料陈述的贡献
- 摘要称，恰当的非高斯系统噪声可同时重现突变与渐变，重尾观测噪声可处理异常值，并展示离散观测等扩展。
- 阅读关注点
- 应核对噪声分布的选择、递推积分与数值近似误差、模型识别程序，以及突变重现与正式变点推断之间的关系。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；示例不能保证任意序列上的效果，计算精度和变点推断条件未说明，不能推断刊本变化。
原文摘要
A non-Gaussian state—space approach to the modeling of nonstationary time series is shown. The model is expressed in state—space form, where the system noise and the observational noise are not necessarily Gaussian. Recursive formulas of prediction, filtering, and smoothing for the state estimation and identification of the non-Gaussian state—space model are given. Also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas. Significant merits of non-Gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples. A typical application of this non-Gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes. Simple Gaussian state—space modeling is not adequate for this situation. Here the model with small system noise variance cannot detect jump, whereas the one with large system noise variance yields unfavorable wiggle. To work out this problem within the ordinary linear Gaussian model framework, sophisticated treatment of outliers is required. But by the use of an appropriate non-Gaussian model for system noise, it is possible to reproduce both abrupt and gradual change of the mean without any special treatment. Nonstandard observations such as the ones distributed as non-Gaussian distribution can be easily treated by the direct modeling of an observational scheme. Smoothing of a transformed series such as a log periodogram can be treated by this method. Outliers in the observations can be treated as well by using heavy-tailed distribution for observational noise density. The algorithms herein can be easily extended to a wider class of models. As an example, the smoothing of nonhomogeneous binomial mean function is shown, where the observation is distributed according to a discrete random variable. Extension to a nonlinear system is also straightforward.