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)

@inproceedings{Macaro2003BayesianIE,
title={Bayesian Identification, Extraction and Forecasting of Unobserved Components for Time Series in the Frequency Domains},
author={Christian Macaro},
year={2003}
}

Figure 10: Prior (dotted line) and posterior (solid line) distributions of the normalization parameters τX , τZ , τε for sunspot data. The prior on the short term component is 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.