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 28: Posterior distributions of the three additive spectra for DJA data. The blue points represent the 95% quintile, the red points represents the 5% quintile, the black solid lines represent observed data (top-left) and the posterior means of the three components (top-right, bottom-left, bottom right). The prior on the short term component (bottom-right panel) is not assumed to be white noise. The hyper-parameters are vX = 10, vZ = 10, vε = 10, v ∗ X = 10, v ∗ Z = 10, v∗ε = 10, 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.