This work aims to present a full Bayesian framework to identify, extract and forecast unobserved components in time series. The major novelty is to present a probabilistic framework to analyze the identification conditions. More precisely, informative prior distributions are assigned to the spectral densities of the unobserved components. This entails a… (More)
Figure 16: Posterior distributions of the three additive spectra for sunspot data. The blue line is the 95% quantile, the red line is the 5% quantile, the black line is the posterior mean and the green dotted line is the prior mean. The prior on the short term component (bottom-right panel) is assumed to be white noise. The hyper-parameters are vX = 0.1, vZ = 0.1, vε = 0.1, v ∗ X = 0.1, v ∗ Z = 0.1, v∗ε = 0.1, τ̃X = σ̂ 2 Y /2π, τ̃Z = σ̂ 2 Y /2π, τ̃ε = σ̂ 2 Y /2π, K = 120, M = 1, and the number of iterations is N = 60000.