Abstract

We present the AdaptSPEC-X method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components parameterized by a time-varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown number of segments and estimates the local log spectra by smoothing splines. AdaptSPEC-X extends AdaptSPEC in three ways. First, through the infinite mixture, it applies to multiple time series linked by covariates. Second, it can handle missing values, a common feature of time series which can cause difficulties for nonparametric spectral methods. Third, it allows for a time-varying mean. Through these extensions, AdaptSPEC-X can estimate time-varying means and spectra at observed and unobserved covariate values, allowing for predictive inference. Estimation is performed by Markov chain Monte Carlo (MCMC) methods, combining data augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo techniques. We evaluate the methodology using simulated data, and describe applications to Australian rainfall data and measles incidence in the United States. Software implementing the method proposed in this article is available in the R package BayesSpec. Supplementary files for this article are available online.

摘要

我们提出了 AdaptSPEC-X 方法，用于联合分析一组可能非平稳的时间序列。该方法是贝叶斯方法，使用协变量相关的无限混合模型来合并多个时间序列，混合成分由时变均值和对数谱参数化。混合成分基于 AdaptSPEC，这是一种非参数模型，它自适应地将时间序列划分为未知数量的片段，并通过平滑样条估计局部对数谱。AdaptSPEC-X 以三种方式扩展了 AdaptSPEC。首先，通过无限混合，它适用于由协变量链接的多个时间序列。其次，它可以处理缺失值，这是时间序列的一个共同特征，可能会给非参数谱方法带来困难。第三，它允许随时间变化的均值。通过这些扩展，AdaptSPEC-X 可以估计观察到的和未观察到的协变量值的时变均值和光谱，从而允许进行预测推理。估计由马尔可夫链蒙特卡罗 (MCMC) 方法执行，结合数据增强、可逆跳跃和黎曼流形哈密顿蒙特卡罗技术。我们使用模拟数据评估该方法，并描述其在澳大利亚降雨数据和美国麻疹发病率方面的应用。R 包 BayesSpec 中提供了实现本文中提出的方法的软件。本文的补充文件可在线获取。和黎曼流形哈密顿蒙特卡洛技术。我们使用模拟数据评估该方法，并描述其在澳大利亚降雨数据和美国麻疹发病率方面的应用。R 包 BayesSpec 中提供了实现本文中提出的方法的软件。本文的补充文件可在线获取。和黎曼流形哈密顿蒙特卡洛技术。我们使用模拟数据评估该方法，并描述其在澳大利亚降雨数据和美国麻疹发病率方面的应用。R 包 BayesSpec 中提供了实现本文中提出的方法的软件。本文的补充文件可在线获取。