Semiparametric Bayesian Inference for Time Series with Mixed Spectra
提出一种半参数贝叶斯方法，将具有平滑谱密度的平稳成分与趋势和周期项的确定性成分相结合，在分层贝叶斯框架下同时估计回归参数、谱密度、未知频率和缺失观测，并构建了检测确定性成分的贝叶斯检验。
Summary A Bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms. The periodic terms may have known or unknown frequencies. The advantage of our approach is that different features of the data—such as the regression parameters, the spectral density, unknown frequencies and missing observations—are combined in a hierarchical Bayesian framework and estimated simultaneously. A Bayesian test to detect deterministic components in the data is also constructed. By using an asymptotic approximation to the likelihood, the computation is carried out efficiently using the Markov chain Monte Carlo method in O(Mn) operations, where nis the sample size and Mis the number of iterations. We show empirically that our approach works well on real and simulated samples.