Bayesian Lattice Filters for Time-Varying Autoregression and Time–Frequency Analysis
Bayesian Lattice Filters for Time-Varying Autoregression and Time–Frequency Analysis
复制标题
用于时变自回归和时频分析的贝叶斯格滤波器
DOI：
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发表时间：
2014
期刊：
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通讯作者：
C. Wikle
中科院分区：
文献类型：
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作者：
Wen;S. Holan;C. Wikle
对非平稳过程进行建模对于许多科学学科（包括环境科学、生态学和金融学等）至关重要。因此，能够在广泛的过程中提供准确估计的灵活方法是人们持续关注的主题。我们提出了一种使用时变自回归模型进行基于模型的时频估计的新方法。在这种情况下，我们采用完全贝叶斯方法，并允许自回归系数和创新方差随时间变化。重要的是，我们的估计方法使用格滤波器并在部分自相关域内进行转换。边际后验分布具有标准形式，并且作为我们的估计方法的方便副产品，我们的方法避免了不需要的矩阵求逆。因此，估计的计算效率极高且稳定。为了说明我们方法的有效性，我们进行了全面的模拟研究，将我们的方法与其他竞争方法进行比较，发现在大多数情况下，我们的方法在估计和真实时变谱密度之间的平均平方误差方面表现出色。最后，我们通过三个建模应用程序展示了我们的方法；即昆虫通信信号、环境数据（风成分）和宏观经济数据（美国国内生产总值（GDP）和消费）。
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time–frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).